1. The problem statement, all variables and given/known data (D^2 + 2D + 1)y = ln(x)/(xe^x) 2. Relevant equations D = d/dx 3. The attempt at a solution First I find the roots of the left side of the equation, -1 of multiplicity 2. This leads to y(c) = Ae^(-x) + Bxe^(-x) Substituting A and B with a' and b' and dividing both sides by e^(-x) I find the two equations: -a' + (1-x)b' = ln(x)/x a' + xb' = 0 Which leads to a' = -ln(x) and b' = ln(x)/x Integrating by parts leads to: a = x(1-ln(x)) b = (1/2)[ln(x)]^2 Which leads to y(p) = ae^(-x) + bxe^(-x) = xe^(-x)[1-ln(x) + (1/2)(ln(x))^2] So y = xe^(-x)[1 - ln(x) + (1/2)(ln(x))^2 + A/x + B] Does this seem correct?