# Thread: Second and third order differential equations

1. ## Second and third order differential equations

I need your help to solve the following differential equations:

1) y''' - y' = e^x

and

2) y'' - xy' = sinx

Thank you,

2. Originally Posted by essedra
I need your help to solve the following differential equations:

1) y''' - y' = e^x

and

2) y'' - xy' = sinx

Thank you,
In both cases substitute v = y'. The first DE becomes second order with constant coefficients. The second DE then gets done using the integrating factor method. Both are in your class notes and textbook.

Then solve for v. And hence solve for y.

If you need more help, please show all that you've done and say where you get stuck.

3. I guess the method is same with the 2nd order diff. equations, so for the non-homogeneous part, I should use Undetermined Coefficients or Variation of Parameters?

4. Originally Posted by essedra
I guess the method is same with the 2nd order diff. equations, so for the non-homogeneous part, I should use Undetermined Coefficients or Variation of Parameters?
Yes.