I am trying to prepare for Undertermined coefficients a portion of differential equations. I have learned insofar to finding a general solution and a particular solution, and setting up a system of equations.
I know that to find a general soltution we must first find a particular and complementary solution:
$$y = y_c + y_p$$
The problem is as follows:
$$y'' - 2y' + y = xe^x$$
I am inclined to use a particular solution
$$y_p = Ax^3e^x + Bx^2e^x$$
but I do not how to proceed, correctly from there. Could someone steer me on the right track? Perhaps show some methods of "good practice"?