Solve the differential equation y" + 3y' + 2y = P1 where, y" = d2y/dx2, y' = dy/dx, P1 = P1(x)) and the initial conditions are y(0) = 0, y'(0) = 0. The input function is given by P1() = { 0, < 0 1, 0 ≤ ≤ 1 0, > 1

Answers

Answer 1

Answer:

[tex]y(x) = 0[/tex]

Step-by-step explanation:

Let P(1) = 0, the differential equation becomes:

y" + 3y' + 2y = 0

Also let y' = my and y'' = m²y

Substitute

m²y+3my+2y = 0

(m²+3m+2)y = 0

The auxiliary equation is expressed as:

m²+3m+2 = 0

Factorize

m²+2m+m+2 = 0

m(m+2)+1(m+2) = 0

(m+1)(m+2) = 0

m+1 = 0 and m+2 = 0

m₁ = -1 and m₂ = -2

Since the value of m is real and distinct, the solution to the differential equation will be expressed as:

[tex]y = C_1e^{m_1x}+C_2e^{m_2x}\\[/tex]

[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\[/tex]

Given the initial condition y(0) = 0

[tex]y(0) = C_1e^{-0}+C_2e^{-2(0)}\\0 = C_1+C_2\\C_1+C_2 = 0 ................. 1[/tex]

If y'(0) = 0

[tex]y'(x) = -C_1e^{-x}-2C_2e^{-2x}\\y'(0) = -C_1e^{-0}-2C_2e^{-2(0)}\\0 = -C_1-2C_2\\C_1-2C_2 = 0...................... 2[/tex]

Solve eqn 1 and 2 simultaneously

From 1:

C₁ = -C₂ .......... 3

Substitute equation 3 into 2:

-C₂-2C₂ = 0

-3C₂ = 0

C₂ = 0

Substitute the constant into the differential equation.

[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\\\y(x) = 0[/tex]


Related Questions

what is 200 times 1238

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Step-by-step explanation:

the answer is 247,600

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Answer: the answer is 247,600

Step-by-step explanation:

what is the graph of the equation Y= 66x - 1200​

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Answer:the answer is b :)

Step-by-step explanation:

Kathrine uses 7/10 of a gallon of red paint to paint 3/5 of her wall. How many gallons of red paint will she use to paint her whole wall?
A.21/50
B.7/15
C.1 1/6
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Answers

Answer:

It is 1 3/10

Step-by-step explanation:

Evaluate: -8/9 + 4/9 - 2/9

A. -14/9
B. -2/3
C. 10/9
D. -1/3

Answers

Answer:

-2/3

Step-by-step explanation:

Add the first two then subtract

The answer to the equation is B, [tex]-\frac{2}{3}[/tex]

First, you must add the the fractions. You add the numerator because all three fractions have like denominators.

[tex]-\frac{8}{9} +\frac{4}{9} -\frac{2}{9}=\frac{6}{9}[/tex]

Then, you must simplify [tex]-\frac{6}{9}[/tex]

[tex]-\frac{6}{9} =-\frac{2}{3}[/tex]

The answer to the equation is [tex]-\frac{2}{3}[/tex]

what is 86,503 written in expanded form​

Answers

Answer:

80,000+6,000+500+3

Step-by-step explanation:

Decode it

Answer:

eighty- six thousand five-hundred and three

Step-by-step explanation:


A 3-yard roll of butcher paper costs $8.55. What is the price per foot?

Answers

Answer:

$2.85

Step-by-step explanation:

8.55/3

Answer:

$2.85 per foot

Step-by-step explanation:

all u gotta do is 8.55/3

Help and brainliest? :(

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Each exterior angle is 120 degrees

I think

find the perimeter of the polygon if

Answers

What are the numbers so I can do the problem.

expand and simplify (x +2)(x+ 1)

Answers

Answer:

x²+3x+3

Step-by-step explanation:

(x+2)(x+1)

x²+x+2x+3

=x²+3x+3

Answer:

x² + 3x + 2

Step-by-step explanation:

Given

(x + 2)(x + 1)

Each term in the second factor is multiplied by each term in the first factor, that is

x(x + 1) + 2(x + 1) ← distribute both parenthesis

= x² + x + 2x + 2 ← collect like terms

= x² + 3x + 2

Find the value of f(-5).
y=f(x)

Answers

Answer:

???

Step-by-step explanation:

???

Jessica prepared 36 kilograms of dough after working 6 hours. How much dough did Jessica prepare if she worked for 8 hours? Assume the relationship is directly proportional.

Answers

Answer:

48

Step-by-step explanation:

because 36 divided by 6 is 6 and that is how much dough she produces in an hour so if you added two more 6s to 6 to make it 8 meaning you are adding 12 because that is how much dough she makes in an hour

The attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot over a weekend. The ratios for the three days were equivalent.

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Saturday there was ???

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5 Aii that answer is 5

Budget Rental Car charges an initial fee of $20 plus an additional $30 per day to rent a car. Enterprise Rental Car charges an initial fee of $36 plus $28 per day. For what number of days is the total cost charged by the companies the same?

I need an answer ASAP!! :)

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Answer:

8 days

Step-by-step explanation:

What is the equation of the following graph

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Answer:

Undefined

Step-by-step explanation:

Explain how to write an equation from a graph in slope intercept form .

Answers

Step-by-step explanation:

To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y-intercept--this should be of the form (0, b). The  y- coordinate is the value of b in the equation.

pls give brainest i only have 2

The slope intercept form is given by y = mx + c

What is the Slope Intercept Form of a Line?

The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

Given here: Slope intercept form

We know that, the equation of a line in point slope form, where (x1, y1) is the point and slope m is:

(y – y₁) = m(x – x₁)

Here, (x, y₁) = (0, c)

Substituting these values, we get;

y – c = m(x – 0)

y – c = mx

y = mx + c

Therefore, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c

Hence, The slope intercept form is given by y = mx + c

Learn more about slope intercept form here:

https://brainly.com/question/29146348

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you earn $25 for washing 5 cars how much do you earn for washing 4 cars

Answers

You will earn $20 washing 4 cars

4(-8x + 5) – (-33x – 26) =

Answers

Answer:

1x + 46 or x + 46

Step-by-step explanation:

4(-8x + 5) – (-33x – 26)

-32x + 20 + 33x + 26

1x + 46

or x + 46

Uh help i don`t get this (ez question) :D

Answers

Answer:

Dividend  divided by Divisor = Quotient

5 divided by 8 = 0.625

Step-by-step explanation:

Verifying the top Awnser that’s pretty much it ^^

The perimeter of a kite can be found using the formula P = 2S + 2L. Which equation expresses S in terms of P and L?

Answers

Answer:

Step-by-step explanation:

P = 2S + 2L

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       2S = P - 2L

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Answer:

0.5P - L

Step-by-step explanation:

P = 2S + 2L

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At the marget 8 apples cost 4 dollars how much does 9 apples cost

Answers

Answer:

 8 /4 = 2

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Answer:

$4.50.

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being a rectangle is a necessary condition for being a square

Answers

Answer:

false

Step-by-step explanation:

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Michael has $1,058.60 in his checking account. He is going to spend $499.66 on a new television, and he will spend the rest on speakers that cost $42.00 each. Which of the following inequalities would determine the maximum number of speakers, x, Michael can buy without spending more money than he has in his account?
help

Answers

Answer:

he can buy 13 speakers.

Step-by-step explanation:

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Roy bought running shoes for $44.98. If the sales tax is 7%, how much did he pay in total?

Answers

Answer:

$48.13

Step-by-step explanation:

before $44.98

sale tax 7.00% or 3.15

after-tax price $48.13

Use the distributive property to simplify the expression, then combine like terms -12 - 5p +2(6p+p)

Answers

Answer:

-12 + 9p

Step-by-step explanation:

Original Equation:

-12 - 5p + 2(6p + p)

Distributive property.

2 x 6p = 12p

2 x p = 2p

Equation:

-12 - 5p + 12p + 2p

Subtract 5p from 12p

-12 + 7p + 2p

Add.

-12 + 9p

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Please consider Brainliest :)

Why is "3 meals a day" a unit rate? it compares 1 meal to 1 day. lt compares 1 meal to 3 days. It compares 3 meals to 1 day. It compares 3 meals to 3 days.​

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Answer:

Compares 3 meals to 1 day

Step-by-step explanation:

The world has made it a basis that most people eat 3 meals a day.

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A trucking company wants to evaluate whether a decrease in the weight of their trucks helps to increase gas mileage. The company randomly selects 100 of their truck drivers, driving trucks that are identical in every way other than weight, to monitor gas mileage over a 1-year period. Results showed an association between truck weight and gas mileage. Which is a possible confounding variable for the provided scenario?

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Answer:

D- the aggressiveness of the driver's driving style

Step-by-step explanation:

Figure B is a scaled copy of Figure A.

Answers

Answer:

1/3

Step-by-step explanation:

On left side its 6:2 so 6/2 is 3

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1/3

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The side that's highest is 9 units, the the image its 3. 3/9= 1/3

DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA

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Answer:

da de da da da de do re mi fa so la mi AAAAAAAAAAA

Step-by-step explanation:

I can speak the language of the gods xD

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Answer:

The answer is B. (2x-3)

the answer to this question is b. 2x-3
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