Find the solution of the differential equation that satisfies the given initial condition. x ln(x) = y 1 + 8 + y2 y', y(1) = 1.

Answers

Answer 1

Answer:

[tex]\mathbf{((lnx)(2x^2)) -x^2 +39 =(2y^2 +(\dfrac{4}{3})(8+y^2)^{3/2})}[/tex]

Step-by-step explanation:

Given that:

[tex]x In(x) = y( 1+ \sqrt{8+ y^2}) \ } \ \dfrac{dy}{dx}[/tex]

[tex]xln(x) *dx= (y+y \sqrt{(8+y^2}) \ dy[/tex]

[tex]\int xln(x) dx = \int(y+y\sqrt{(8+y^2})) \ dy[/tex]

[tex]\int lnx (x)dx =(\dfrac{y^2}{2} +\dfrac{1}{3}(8+y^2^{)3/2})[/tex]

[tex](lnx \dfrac{x^2}{2})-\int((\dfrac{x^2}{2})\times \dfrac{1}{x} =(\dfrac{y^2}{2} +\dfrac{1}{3}(8+y^2)^{3/2})[/tex]

[tex]((lnx)(\dfrac{x^2}{2}))-\int(\dfrac{x}{2}) =(\dfrac{y^2}{2} +(\dfrac{1}{3})(8+y^2)^{3/2})[/tex]

[tex]((lnx)(\dfrac{x^2}{2}))-(\dfrac{x^2}{4}) +C= (\dfrac{y^2}{2 }+(\dfrac{1}{3})(8+y^2)^{3/2})[/tex]

For  y(1) = 1

[tex]((ln(1))(\dfrac{1^2}{2}))-(\dfrac{1^2}{4}) +C= (\dfrac{1^2}{2 }+(\dfrac{1}{3})(8+1^2)^{3/2})[/tex]

[tex](0)-(\dfrac{1}{4}) +C =(\dfrac{1}{2} +(\dfrac{1}{3})(3)^3)[/tex]

[tex]C=(\dfrac{19}{2}) +(\dfrac{1}{4})[/tex]

[tex]C=\dfrac{39}{4}[/tex]

[tex]((lnx)(\dfrac{x^2}{2}))-(\dfrac{x^2}{4}) +(\dfrac{39}{4}) = (\dfrac{y^2}{2} +(\dfrac{1}{3})(8+y^2)^{3/2})[/tex]

[tex]\mathbf{((lnx)(2x^2)) -x^2 +39 =(2y^2 +(\dfrac{4}{3})(8+y^2)^{3/2})}[/tex]


Related Questions

Let see if this work

Answers

Answer:

i really dont know what you are saying, but thanks for the points and have a nice day! always smile peeps!

Find the volume of a right circular cone that has a height of 15.2 cm and a base with a diameter of 11.9 cm. Round your answer to the nearest tenth of a cubic centimeter.

Answers

9514 1404 393

Answer:

  563.5 cm³

Step-by-step explanation:

Use the formula for the volume of a cone:

  V = (1/3)πr²h

Recognize that the radius is half the diameter:

  r = (11.9 cm)/2 = 5.95 cm

  V = (1/3)π(5.95 cm)²(15.2 cm) ≈ 563.516 cm³

The volume of the cone is about 563.5 cm³.

_____

Additional comment

If you use 3.14 for the value of π, then the result will be 563.2 cm³.

write a polynomial equation for each set of roots 5 and 7

Answers

Answer:

x²-2x-35

Step-by-step explanation:

(x-7)(x+5)

x²+5x-7x-35

x²-2x-35

HELP PLEASEEEEEEEEEEEEEEE ITS A GRADE

Answers

Answer:

1. b

2. d

3. a

4. A

Step-by-step explanation:

Answer: ITs A

Step-by-step explanation:

Because they are all real numbers and the other options are incorrect

I need help, please
it is do tomorrow

Answers

Answer:

21 millimeters

Step-by-step explanation:

ummmm yes

Sasha made cups of lemonade to sell at her stand. She sold 9 cups of lemonade in the first hour. For each hour after that, she sold five cups. She was outside for a total of 4 hours. How many cups of lemonade did she sell?

Answers

Answer:

first hour=9 cups

the next three hours,five cups each=15 cups

15+9=24 cups

The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests ​negative, given that he or she has the disease.

Answers

Answer:

[tex]Probability = 0.0470[/tex]

Step-by-step explanation:

This question has missing detail. (See attachment for the data)

Required

Determine the probability that a selected individual who has the disease test negative.

This type of probability is referred to as conditional probability.

First, we need to get the number of individuals who have the disease.

[tex]Disease =142 + 7[/tex]

[tex]Disease =149[/tex]

Next, we list out the number of individual who have the disease but is negative.

[tex]Negative = 7[/tex]

The probability is then calculated as:

[tex]Probability = \frac{Negative}{Disease}[/tex]

[tex]Probability = \frac{7}{149}[/tex]

[tex]Probability = 0.04697986577[/tex]

[tex]Probability = 0.0470[/tex] (approximated)

If the coefficient of determination is 0.394, what percentage of the data about the regression line is unexplained

Answers

Answer:

The percentage [regression line is unexplained]  = 60.6%

Step-by-step explanation:

Given:

Coefficient of determination = 0.394

Find:

The percentage [regression line is unexplained]

Computation:

Coefficient of determination = 0.394

Coefficient of determination = 39.4%

The percentage [regression line is unexplained]  = 100% - Coefficient of determination

The percentage [regression line is unexplained]  = 100% - 39.4%

The percentage [regression line is unexplained]  = 60.6%

Please help i was crying :(
Also there is another one
“Subtract. Write Your answer in simplest form” which is: 6 3/4 - 2 3/20

Answers

4 and 3 fifths i think 4 3/5

Answer:

is it 4 3/5 it might be

Step-by-step explanation:

What is a fraction equivalent to 4/4? Explain how you know.

Answers

Answer:  Any number over itself is equivlent to 4/4.

Examples: 3/3, 18/18, 5/5, 90/90

Step-by-step explanation:

Because 4/4 is equivalent to 1 whole.

A fraction that is equivalent to 4/4 would be, 5/5 as, After simplifying the fraction 5/5 is equal to 1.

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction.

Given that,

The fraction is,

⇒ 4/4

Now, after simplifying the fraction we get;

⇒ 4/4

⇒ 1

So, Let a fraction that is equivalent to 4/4 would be;

⇒ 5/5

After simplifying we get;

⇒ 5/5 = 1

Therefore, A fraction that is equivalent to 4/4 would be, 5/5

To learn more about the fraction visit:

https://brainly.com/question/5454147

#SPJ6

solve the simultaneous equations
5x + 6y = 3
2x - 3y = 12

Answers

Answer: x =3; y = -2

[tex]\left \{ {{5x+6y=3} \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {2.\frac{3-6y}{5}-3y =12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {6-12y-15y=12.5}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {17y=6-60=-54}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {y=-54/27}} \right.\\\\\\ <=>\left \{ {{x=\frac{3-6y}{5} } \atop {y=-2}} \right.\\\\<=>\left \{ {{x=3} \atop {y=-2}} \right.[/tex]

Step-by-step explanation:

Answer:

x = 3, y = -2.

Step-by-step explanation:

5x + 6y = 3

2x - 3y = 12           Multiply this by 2:

4x - 6y = 24           Now add this to the first equation:

9x = 27

x = 3.

Substitute x = 3 in the second equation:

2(3) - 3y = 12

-3y = 12 - 6 = 6

y = 6 / -3

y = -2.

Adam divides 8032 x 32 in which place write the first digit of the quotient

Answers

Answer:

100

Step-by-step explanation:

8032\32

what is the length of a chord at a distance for 4 cm away from the centre of a circle of radius 5 cm​

Answers

See attachment for math work.

We must reject x = -3 because distance is positive.

The value of x is 3.

Chord = 2x

Chord = 2(3)

Chord = 6 cm

An adult elephant drinks about 225 liters of water each day

Answers


Okay ? What’s the question
I don’t understand like what do you mean with it?

(16, 2) and (32, 4) rate of change

Answers

Answer:

m = 1/8

Step-by-step explanation:

Assuming that you mean the slope:

[tex]m=\frac{rise}{run}=\frac{4-2}{32-16}=\frac{2}{16}=\boxed{\frac{1}{8}}[/tex]

Hope this helps.

Cindy bought 3 burgers and 2 soft drinks for $10.50. At the same restaurant, Sean bought 4 burgers and 3 soft drinks for 14.50. How much does 1 burger cost

Answers

Answer:

To much to count

Step-by-step explanation:

PLEASE HELP!!! TIMED TEST!

Which pair of angles must be supplementary?
1 and 6
2 and 5
5 and 4
6 and 2

Answers

Answer:

ok supplementary angles are two angles when they add up upto 180 degree so angle 2 and 5 make 180 degree .

What is
0.74314482
as a fraction?

(I don’t have my TI Calculator with me and that is what I need to figure out this question)

Answers

The answer is

3715731 over 5000000

A bowl holds 4 cups of rice if I use a measuring cup that holds 1/8 of a cup how many times will I need to fill the measuring cup in order to fill the entire bowl

Answers

Answer:

32 times

Step-by-step explanation:

It's SUPER easy, all you have to do is take that 1/8 and make it into a regular 8. Now all you do is multiply 4 by 8.

I know there's probably some way the teachers taught that's so much harder then it already is, but if you try to look at it from an easier perspective, you'll be a pro!

Try some more so you'll slowly start getting better at them! Anyway I hope this helped!!

Calcular el valor de x en la siguiente figura

Answers

Answer:

demos los

Step-by-step explanation:

Chris is trimming trees. He can trim 2/3 of a tree in 1/2 of an hour. At what rate can Chris trim trees​

Answers

Answer:

1 tree every 45 mins

Step-by-step explanation:

Answer:

he trims i 1 and 1/3 trees an hour

it would take him 45 minutes to trim 1 tree

Step-by-step explanation:

Determine whether the function g(x)= -x +2 is increasing or decreasing.​

Answers

Answer:

its decreasing :) the person above me is correcto

5 What is the value of m? Show your work 3 5 (2m - 5) = 2(3m - 4)​

Answers

Answer:

70m-175=6m-12

70m-6m=175-12

64m=163

m=163/64

What is the most profound problem in maths?
No answer needed, just take the points.

Answers

Answer:

SWEEEET!!

Step-by-step explanation:

:D

Answer:thx so much I needed them

Step-by-step explanation:

Boden's account has a principal of $700 and a simple
interest rate of 3.7%. Complete the number line. How much
money will be in the account after 4 years, assuming Boden
does not add or take out any money?

Answers

Answer:

823.2

Step-by-step explanation:

Interest = 700 × 4.4/100 × 4 = 123.2

Balance = Principle + interest

700 + 123.2 = 823.2

Answer - 823.2

Hope this helps!!!

42 kids bought popcorn at the movie. This was 60% of the kids who attended the movie.
How would you summarize the process to find the number of kids who attended the
movie?

Answers

Answer:

Total number of children = 70

Step-by-step explanation:

Given:

Number of kids buy popcorn = 42

Percent of kids buy popcorn = 60% = 0.6

Find:

Total number of children

Computation:

Total number of children = Number of kids buy popcorn / Percent of kids buy popcorn

Total number of children = 42 / 0.6

Total number of children = 70

Fill in the missing reason in proof.

Answers

Answer:

SAS

Step-by-step explanation:

As per steps given the congruent pairs are:

AB and ACBD and CDAngle B and angle C

So two sides and included angle - it represents side-angle-side or SAS congruency theorem

Car dealership pays a wholesale price of $10,000 to purchase a vehicle if they mark up the price 20% what is the retail price of the car

Answers

Answer:

8000

Step-by-step explanation:

10000 x 20% = 2000

10000-2000= 8000

Which expression is equivalent to 8(x + 2)?
(A was wrong) C 8x + 16
B 8 + x + 8 + 2 D 8x + 10

Answers

i believe it is C when you distribute: 8*x is 8x and 8*2 is 16
I’m 80% sure is C ....

What is the slope of the line that passes through the points E(5, 1) and F(2-7)?
12 Points)

Answers

Answer:

8/3

Step-by-step explanation:

the slope is 8/3 i am sure

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