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# Differential equation watch

1. Need help with question 3.

Not entirely sure how to do it do i need to find an integrating factor?
2. (Original post by Super199)
Need help with question 3.

Not entirely sure how to do it do i need to find an integrating factor?
Might be helpful to take a picture of, or link to the question.
3. (Original post by Kvothe the arcane)
Might be helpful to take a picture of, or link to the question.
Well i tried uploading it but it wont let me so i shall type it out.

3. Find the general solution of the differential equation dy/dx-3x^2y= xe^(x^3), giving y explicitly in terms of x. Find also the particular solution for which y=1 when x=0
4. (Original post by Super199)
Need help with question 3.

Not entirely sure how to do it do i need to find an integrating factor?
where is the question
5. (Original post by Super199)
Well i tried uploading it but it wont let me so i shall type it out.

3. Find the general solution of the differential equation dy/dx-3x^2y= xe^(x^3), giving y explicitly in terms of x. Find also the particular solution for which y=1 when x=0

The integrating factor is

Work it out and the equation by it.
6. (Original post by Kvothe the arcane)

The integrating factor is

Work it out and the equation by it.
If i could upload a picture it would help but i got the integrating factor as e^-x^3.

Multiplied through :

Dy/dxe^-x^3 - 3x^2ye^-x^3= x

D/dx(ye^-x^3)=x

Ye^-x^3= x^2/2+c.
Im having troubles with e. If you divide by e^(-x^3) do you get y= (x^2+c)e^x^3
7. (Original post by Super199)
If i could upload a picture it would help but i got the integrating factor as e^-x^3.

Multiplied through :

Dy/dxe^-x^3 - 3x^2ye^-x^3= x

D/dx(ye^-x^3)=x

Ye^-x^3= x^2/2+c.
Im having troubles with e. If you divide by e^(-x^3) do you get y= (x^2+c)e^x^3
So you have
Perhaps rewrite as ?
8. (Original post by Kvothe the arcane)
So you have
Perhaps rewrite as ?
Got it cheers need help with another if you dont mind. Im having trouble with the integrating factor again.

Dy/dx +y/(xlnx)= 1/x. With y=1 when x=e is to be solved using an integrating factor. Find the integrating factor and solve the differential equation. Sketch the solution curve for x>1.
Integral of xlnx im not sure. Do i have to use parts? But the problem is it is (xlnx)^-1. So not sure. Or can i write it as 1/x*lnx. Idk cheers
9. (Original post by Super199)
Got it cheers need help with another if you dont mind. Im having trouble with the integrating factor again.

Dy/dx +y/(xlnx)= 1/x. With y=1 when x=e is to be solved using an integrating factor. Find the integrating factor and solve the differential equation. Sketch the solution curve for x>1.
Integral of xlnx im not sure. Do i have to use parts? But the problem is it is (xlnx)^-1. So not sure. Or can i write it as 1/x*lnx. Idk cheers

But it might be helpful to recall that and .

Not IBP, no.
10. (Original post by Kvothe the arcane)

But it might be helpful to recall that and .

Not IBP, no.
I cant see the link sorry. I know that lnx integrates to xlnx-x and also what you said. But I cant see the link
11. (Original post by Super199)
I cant see the link sorry. I know that lnx integrates to xlnx-x and also what you said. But I cant see the link

What is the relationship between 1/x and lnx? And how might that be related to what I wrote above?
12. (Original post by Super199)
Got it cheers need help with another if you dont mind. Im having trouble with the integrating factor again.

Dy/dx +y/(xlnx)= 1/x. With y=1 when x=e is to be solved using an integrating factor. Find the integrating factor and solve the differential equation. Sketch the solution curve for x>1.
Integral of xlnx im not sure. Do i have to use parts? But the problem is it is (xlnx)^-1. So not sure. Or can i write it as 1/x*lnx. Idk cheers
Use the substitution , you'll end up with .
13. (Original post by Zacken)
Use the substitution , you'll end up with .
Right that helps now how do you integrate lnx/x
14. (Original post by Super199)
Right that helps now how do you integrate lnx/x
Not to worry got it. Using parts
15. (Original post by Super199)
Right that helps now how do you integrate lnx/x
I'm not sure what you're asking. You want to integrate , right? That's .

Integrating is an easy one if you use you should get

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