Thread: Solving a first order DE

Hello,

I am trying to solve this problem:
x(dy/dx)-2y=x^15
By bringing this to the standard form I get:
(dy/dx)-(2/x)y=x^14
Now I multiply the equation by (1/x^2)
I get the form d/dx(y/x^2)=(x^12)
Integrating both sides I get: (y/x^2)=((x^13)/13)+C(x^2)

Now I tried using the condition y(1)=-2 to get the value of C. However, every time I get the value of C to be 1, unfortunately this is not the right answer.

Where am I going wrong, any help would be highly appreciated.

Thanks!

Originally Posted by sgupta

Hello,

I am trying to solve this problem:
x(dy/dx)-2y=x^15
By bringing this to the standard form I get:
(dy/dx)-(2/x)y=x^14
Now I multiply the equation by (1/x^2)
I get the form d/dx(y/x^2)=(x^12)
Integrating both sides I get: (y/x^2)=((x^13)/13)+C(x^2)

Now I tried using the condition y(1)=-2 to get the value of C. However, every time I get the value of C to be 1, unfortunately this is not the right answer.

Where am I going wrong, any help would be highly appreciated.

Thanks!

Assuming what you have for the general solution is correct:



Put :



CB