Hi! I am looking through some solved exercises. One of them is the following: Solve the equation: x^2 y'' + (x^2 - 3x)y' + (3-x)y = x^4 knowing that y=x is a solution of the homogeneous equation. The professor then solves it by doing the following substitution: y=xz. Then he calculates y' and y'', substitutes, etc. What I do not understand is, how do you know, from the fact that y=x is a solution to the homogeneous equation, that you have to do that substitution y=xz?