Find the general solution of the given higher-order differential equation. y''' + 3y'' + 3y' + y = 0

Answers

Answer 1

Answer:

[tex]y(x)=c_1e^{-x}+c_2xe^{-x}+c_3x^2e^{-x}[/tex]

Step-by-step explanation:

We can determine the characteristic equation all we have to do is:

let y' = m, hence y" = m², y'" = m³

Therefore, the higher-order differential equation becomes:

m³ + 3m² + 3m + 1 = 0

(m + 1)(m² + 2m + 1) = 0

(m + 1)(m + 1)(m + 1) = 0

(m + 1)³ = 0

m = -1, -1, -1

Therefore the general solution is given as:

[tex]y(x)=c_1e^{-x}+c_2xe^{-x}+c_3x^2e^{-x}[/tex]

[tex]c_1,c_2,c_3\ are\ constants.[/tex]


Related Questions

translate the sentence into an equation

The sum of 6 times a number and 2 is equal to 3

Answers

Answer:

6x + 2 = 3

Step-by-step explanation:

x would represent the unknown number

The sum refers to addition

6 times a number would be 6x (you can use any variable, but for this example I'm using x)

When you put it all together, it is 6x + 2 = 3

The required equation is 6x + 2 = 3.

It is required to find the equation.

What is equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers

Given:

The sum of 6 times a number and 2 equals 3.

According to given question we have,

Let the number be x.

6 times a number would be

6x

The sum of 6 times a number and 2 equals 3.

6x + 2 = 3.

Therefore, the required equation is 6x + 2 = 3.

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34 full. He uses 16 of a full tank’s gas per day driving to and from work.

How many days can Drew drive to work with the gas he has in the tank?

Answers

He can go one day with the gas he has

I need help with mixed numbers when subtracting plz

Answers

Answer:

turn it into an improper fraction then subtract

Step-by-step explanation:

5×6=30

30+1=31

31/6

3×6=18

18+5=21

21/6

31/6 - 21/6 = 10/6

simplify: 5/3 ♡

I'm not sure tho lol

hello I need help on it ​

Answers

It would be 78/4=19.5 which would mean that he would be able to set 19 tables. To be able to set all of the tables he would need 2 more napkins because 19*4=76. 78-76=2 so they would need 2 more to finish the last table.

A diver swims 5.875 feet up to the surface of the water. Which number represents the diver’s position in relation to the surface before swimming to the top?
-5.9 feet
Negative 5 and three-fourthsfeet
-58 feet
Negative 5 and StartFraction 7 over 8 EndFractionfeet

Answers

Answer:

Negative 5 and 7 over 8

Step-by-step explanation:

Answer:

Negative 5 and StartFraction 7 over 8

Step-by-step explanation:

How do I write 4,332 in scientific notation??

Answers

Answer:

4.332 x 10 to the 3 power I do believe

Step-by-step explanation:

Answer:

4.332 times 10^3

Step-by-step explanation:

ion kno if thats right but i tried.

question 10 I mark as brainliest ​

Answers

Answer:

134 is the answer

Answer: 134

Step-by-step explanation:

54+ (48+72) x 2/3

54+120x2/3=134

3 5 of students at a school are boys. If there are 2610 students at the school, how many are girls?

Answers

Answer:

1044 girls in the school

Step-by-step explanation:

3/5*2610=1566 boys

2610-1566-1044 girls

it should be 1044 because

3/5=.6 or 60%boys and 40% girls

2610 * 60% or .6 = 1566 boys

2610 - 1566boys = 1044 girls

or

2610 * 40% or .4 = 1044 girls

so there are 1044 girls at the school

what is the sale tax on a $14,500 truck if the tax rate is 9%​

Answers

Answer:

$15, 805.00

Step-by-step explanation:

Tax is based on the state you live in.

The capacity of a dump truck is listed by the manufacturer as 10 yd3 . A construction site requires the removal of of dirt, and the contractor has four identical trucks. How many trips will each need to make

Answers

Question:

The capacity of a dump truck is listed by the manufacturer as 10 yd^3. A construction site requires the removal of 200 m^3 of dirt, and the contractor has three identical trucks. How many trips will each need to make?

Answer:

7 trips

Step-by-step explanation:

Given

[tex]Capacity = 10yd^3[/tex]

[tex]Dirts = 200m^3[/tex]

[tex]Trucks = 4[/tex]

Required

Determine the number of trips of each truck

Divide the volume of dirts by 4 to get the portion of each truck

[tex]Each\ Truck = \frac{200m^3}{4}[/tex]

[tex]Each\ Truck = 50m^3[/tex]

Divide the portion of each truck by capacity of each truck to get the number of trip

[tex]Trip = \frac{50m^3}{10yd^3}[/tex]

Convert m^3 to yd^3

[tex]Trip = \frac{50 * 1.30795yd^3}{10yd^3}[/tex]

[tex]Trip = \frac{65.3975yd^3}{10yd^3}[/tex]

[tex]Trip = \frac{65.3975}{10}[/tex]

[tex]Trip = 6.53975[/tex]

Approximate:

[tex]Trip = 7[/tex]

Help me please is the math

Answers

Answer:

2nd) which is 4 multiplied by 5 multiplied by 2


The area of a parallelogram is 24 square units. One side of the parallelogramis
36 units long. The other side is 4 units long. Which could be the parallelogram's
height? Choose all the correct answers.
A.1/6
B.2/3
C.3/2
D.6
E.9

Answers

In this particular Equationthe answere is c

The required height of the parallelogram is 2/3. Option B is correct.

Given that,
The area of a parallelogram is 24 square units. One side of the parallelogramis 36 units long. The other side is 4 units long. Which could be the parallelogram's height is to be determined.

What is parallelogram?

A parallelogram is a quadrilateral consisting of pairs of parallel side.

Here,
We have given the area of the parallelogram and the measure of its base. So,
Area of the parallelogram = base * height
                                       24 = 36 * height
                                       height = 2 / 3

Thus, the required height of the parallelogram is 2/3. Option B is correct.
 

                           

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M/x =n-p, x for p ??

Answers

Answer:

the answer is A) X=m/n-p

Step-by-step explanation:

m/x=n-p

n-p=m/X

(n-p)×x=m

X=m/n-p

Answer this please and thank you

Answers

Answer:

The Answer is x^2/2

Step-by-step explanation:

The ^ is the power of _

In this case ^ is the power of 2.

For a certain type of sand, 1 cubic foot weighs 80 pounds. The sand goes in a container that weighs 40 pounds. Use the Ray tool to make a graph that shows the total weight of the container and sand, w, filled with n cubic feet of this sand. I need the coordinates for the graph please.

Answers

Answer:

First, let's write our equation in a general way.

We know that:

1 cubic foot weighs 80 pounds.

The container weighs 40 pounds.

Then, if i put n cubic feet of sand in the container, the total mass will be one time the mass of the container plus n times the mass of one cubic foot of sand.

We can write this as:

w(n) = 40lb + n*80lb

This is a linear equation, where the y-axis will represent the mass in pounds and the x-axis will be the number of cubic feet of sand in the container in units, a graph of this is shown below.

You can see that it is really steep, this is because for really small increments in n, the weight increases a lot.

Answer

ok, Just plot the points at (0,40) and (2,200) :))

4(3x + 1)
What is the answer to 4(3x + 1)

Answers

12x + 4

Divide 12 by 4

X=3

Answer:

Answer is 12x+4. Hope that helped.

Sub to SZ Lexrn if that does not show search up shiyo on vr and first vid is them please help out , thx bye . If you do it cmt and ill make a post for yall for 100 points, so my friends won't amke fun of me

Answers

Answer:

If it counts as a question, lol sure, I'd love to help

Since there are no exponents in this problem, the next step is
✔ (- 2)2.2
.
Simplify the previous step and you get
.
The final answer is

Answers

If the check mark is a square root the next step is -2 x 2.2

Anwers:

22    is the answer

I need help with Number 7 please!!!

Answers

Answer:

8.06 ft or [tex]\sqrt{65}[/tex]  ft

Step-by-step explanation:

Since Rebecca bought a square table and squares have equal sides, you can take the square root of the area of the table, which gives you [tex]\sqrt{65}[/tex]  ft per side. This can be approximated to 8.06 ft.

8.06 ft
Mark me as the brainliest please I spent 25 hours working on this. Thank you very much little boo. You are so segsy. Go get some Bob pics from mother’s boyfriend. 8.06 under your di37 hole

An oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day. For each additional well that is drilled, the average production per well decreases by 25 barrels per day.

Required:
How many additional wells should be drilled to obtain the maximum amount of oil per day?

Answers

Answer:

The additional wells for maximum amount of oil per day is 3 wells.

Step-by-step explanation:

Given;

initial number of wells, n = 6

total production, T = 1800

average production per well, = 1800/6 = 300 barrels per day

Let the additional well = y

total number of wells after optimization = 6 + y

new production per well = 300 - 25y

new total production = (6+y)(300-25y)

t = 1800 - 150y + 300y - 25y²

t = 1800 + 150y - 25y²

dt / dy = 150 -50y

for maximum value, dt/dy = 0

150 - 50y = 0

50y = 150

y = 150 / 50

y = 3

Therefore, the additional wells for maximum amount of oil per day is 3 wells.

33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.

Given that an oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day, and for each additional well that is drilled, the average production per well decreases by 25 barrels per day, to determine how many additional wells should be drilled to to obtain the maximum amount of oil per day, the following calculation must be performed:

1800 x 6 = 10800 1200 x 30 = 36000 1000 x 38 = 38000 950 x 40 = 38000 900 x 42 = 37800 975 x 39 = 38025

Therefore, 33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.

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Is this a function or not a function? (Picture)

Answers

Answer:

Not a Function

Step-by-step explanation:

Lilliana is training for a marathon. She runs the same distance every day for a week on Monday,
Wednesday, and Friday, she runs 2 laps on a running trail and then runs 6 more miles. On Tuesday and
Sunday, she runs 4 laps on the trail and then runs 2 more miles. On Saturday, she just runs laps. How
many laps does Lilliana run on Saturday?

Answers

Answer: 6 miles

Step-by-step explanation:

WEDNESDAY + FRIDAY (# OF MILES)

The Miles Covered by Each Lap = 3x

The Miles on Top of That = 6

TUESDAY + SUNDAY (# OF MILES)

The Miles Covered by Each Lap = 5x

The Miles on Top of That = 2

You want to now put that into an equation! Therefore, you want to put the number of miles from Wednesday and Friday on one side and the number of miles from Tuesday and Sunday on the opposite side.

SOLVING EQUATION FOR MILES PER LAP

Step 1) 3x + 6 = 5x + 2

given equation from what we put together.

Step 2) -3x + 3x + 6 = 5x + 2 -3x

subtract 3x from both sides.

Step 3) -2 + 2x + 2 = 6 -2

subtract 2 from both sides.

Step 4) 2 × x = 4

divide both sides by 2 because you want to put the variable (x) on one side.

Step 5) x = 2 miles for each lap

Now you want to go look back at the equation and plug in 2 for the variable x.

Step 6) 5 ×2 + 2 = 12

PEMDAS!

Step 7) 12 ÷ 2 = 6

SHE RUNS 2 MILES ON SATURDAYS!

how do I write an equation in standard form with the points (3,3) (0,-3) (2,-3)

Answers

First:
-3-3= -6 2-3=-1
-6/-1=6

Y=6x+b
3=6 x 3
3=18

Subtract both sides by 18

B=-15

Answer= y=6x-15

Sharon wants to open a checking account from which to pay bills. She wants online services, and a debit card, which both banks provide for free. Based upon past experience, she expects to accidentally overdraft the account 1 time per year, due to unexpected charges and miscommunications. She expects no 2nd copies of statements, and to use network ATMs 4 times per month with either bank. She has $3300 in an emergency savings account at First State Bank, and thinks that the balance will be enough to cover overdrafts in the future if automatic transfers are made when needed.

Answers

Answer:

a.No, Common Bank will save Sharon more money.

Step-by-step explanation:

There are two banks i.e. first state bank and the common bank that should be compared in the table depend upon the prices of both the banks

On seeing it we get to know that the first state bank would charged a fee on a monthly basis i.e. $4 while on the other hand the common bank has no fee on the monthly basis

Also the unsufficient bonds are more cheaper in the common bank if we compared with the first state bank

Moreover, the $7 is charged in the first state bank and $3 charged in the common bank.

Therefore the common bank would become cheaper

Hence, the correct option is a.

Answer:

Sharon wants to open a checking account from which to pay bills. She wants online services, and a debit card, which both banks provide for free. Based upon past experience, she expects to accidentally overdraft the account 1 time per year, due to unexpected charges and miscommunications. She expects no 2nd copies of statements, and to use network ATMs 4 times per month with either bank. She has $3300 in an emergency savings account at First State Bank, and thinks that the balance will be enough to cover overdrafts in the future if automatic transfers are made when needed.

A 4-column table with 5 rows. Column 1 is labeled First State Bank with entries monthly fee, non-sufficient funds fee, second copy of statement, network A T M usage, non-sufficient funds protection from a First State Bank savings account. Column 2 is labeled Description with entries 4 dollars, 36 dollars, 7 dollars, 3 dollars each transaction, 4 dollars on each day that a transfer occurs to cover an overdraft. Column 3 is labeled Common Bank with entries monthly fee, non-sufficient funds, second copy of statement, network A T M usage, non-sufficient funds protection from a Common Bank savings account. Column 4 is labeled Description with entries 0 dollars, 24 dollars, 4 dollars, 2 dollars each transaction, not offered with this account.

Based on the tables of fees, above, if Sharon chooses First State Bank, will it save her money over choosing Common Bank?

a.   No, Common Bank will save Sharon more money. <<<---Correct b.   Yes, First State Bank will save Sharon money. c.   No, First State Bank and Common Bank would have the same costs for Sharon. d.   No, costs cannot be estimated in advance, so this information cannot be used.

Step-by-step explanation:

Edge 2021

the first 5 multiples of 18 after 0 are?​

Answers

Answer:

18,36,54,72,90 are first five multiples of 18

Step-by-step explanation:

Answer:

18,36,54,72,90

Step-by-step explanation:

5d+1/2=d-4 section 2.04

Answers

Answer:  d = -9/8

Steps: 5d + ½ = d - 4

Subtract ½ from both sides: 5d + ½ - ½  = d - 4 - ½

Simplify: 5d = d - 9/2

Subtract d from both sides: 5d - d = d - 9/2 - d

Simplify: 4d = -9/2 ÷ 4

Simplify: d = -9/8

PLz mark brainliest:)

Equivalent Expressions

Warm-Up

Active

Evaluating an Expression

Complete the statements.

Evaluate (15 - 4x) + 5 when x = 3.

Substitute the given value for the

Evaluate within

parentheses.

to simplify.

Use the

inside the

Evaluate exponents.

First, complete the

parentheses.

Next, complete the

parentheses.

Last, complete the addition.

inside the

Multiply and divide

from left to right.

The value is

Add and subtract

from left to right.

Answers

Answer:

Complete the statements.

Substitute the given value for the

✔ variable

.

Use the

✔ order of operations

to simplify.

First, complete the  

✔ multiplication

inside the parentheses.

Next, complete the

✔ subtraction

inside the parentheses.

Last, complete the addition.

The value is

✔ 8

.

Step-by-step explanation:

Plz give me brainlest

Answer:

Variable, order of operations, multiplication, subtraction, 8.

Step-by-step explanation:

Got it right Edge2021

Real Estate Agent:

A woman bought 4 lots for $48,000 each. She then subdivided

them into a total of 7 lots that sold for $33,000 each. What was

her percent of profit? I

Savings and Loan Counselor:

A customer wishes to borrow $30,000, make monthly payments

of interest only, and pay the full amount of the principal at the

end of the term. If the interest rate is 12% annually, what are the

monthly payments for a five-year term?

Answers

Step-by-step explanation:

A.

Cost of 4 lots for $48,000= 48000*4

=$192,000

Sales made from all 7 lots = 33000*7

= $213,000

Profit =213,000-192,000

Profit =$39,000

Percent profit =(39000/192000) *100

=0.20*100

=20%

B.

Total interest formula=

Principal Loan Amount x Interest Rate x Time

Interest =30000x0.12x5

Interest = $18,000

Monthly payments for 5 years

= 18000/12*5

=18000/60

=$300

At a school, there are 120 athletes. The ratio of boy athletes to giri athletes is 3:5. How many of the athletes are girls?
А
75
B
45
с
24
D 5

Answers

Answer:

a

Step-by-step explanation:

because there are over half girls and half of 120 is 60 and 75 is over half

How can you use the order of operation to explain why you cannot combine the variable terms before using the distributive property when solving the equation 7(x+5)-x=42

Answers

Answer:

Step-by-step explanation:

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.

Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.

Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.

Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.

Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways

We cannot combine the variable terms before using the distributive property when solving the equation as it will results in wrong answer.

What is distributive property of multiplication over addition ?

If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.

Here the expression given is :

7(x+5)-x=42

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.

Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.

Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways.

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