Find all solutions for the following ODE:
I figured it might be easier to solve as:
but that still has me somewhat confused.
Now, search for a single solution to the entire equation. Normally, I would suggest something of the form y= A cos(wx)+ B sin(wx) but after you have solved the corresponding homogeneous equation, you may see why you should try y= A x cos(wx)+ B x sin(wx) instead. Find y" for that, put into the equation and solve for A and B.
The general solution to the entire equation is the sum of the general solution to the corresponding homogeneous equation and any single solution to the entire equation.