Hi I have problem to answer this question. I think that it is a question of recognizing the right solution rather than computing. Give the general solution of the differential equation: y'' -6y'+9y=-5e(3x)+(1/x)e(3x) 1- y=C1*e(3x)+C2*x*e(3x)-(5/2)x2*e(3x)+x*e(3x)*ln(x) 2- y=C1*e(3x)+C2*x*e(3x)-(5/2)x*e(3x)-x*e(3x)*ln(x) 3-y=C1*e(3x)+C2*x*e(3x)-(5/2)*e(3x)+e(3x)*ln(x) My problem is when to know if the particular solution is multiply by x or x^2. when the particular solution is a solution of the homogenous equation , we multiply the particular solution by x. when do we multiply by x^2?? Can you give me a quick example please?? Thank you B.