Find the general solution of
First, solve the homogeneous equation . It implies : writing the characteristic equation and finding its root. Then, using these roots, you can deduce an expression of the solution .
Then, find a particular solution of . It can be achieved by showing that is a solution for some value of . (usually, if the second member is a polynomial of searching for a particular solution of this form works well)
The solution of the complete equation will be the sum .