ODE
\[ x^2 y''(x)-x^2 y'(x)-2 x^2 y(x)=2 x^2 \log (x)+x+1 \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.249562 (sec), leaf count = 26
\[\left \{\left \{y(x)\to -\log (x)+c_1 e^{-x}+c_2 e^{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.082 (sec), leaf count = 21
\[[y \left (x \right ) = {\mathrm e}^{-x} \textit {\_C2} +{\mathrm e}^{2 x} \textit {\_C1} -\ln \left (x \right )]\] Mathematica raw input
DSolve[-2*x^2*y[x] - x^2*y'[x] + x^2*y''[x] == 1 + x + 2*x^2*Log[x],y[x],x]
Mathematica raw output
{{y[x] -> C[1]/E^x + E^(2*x)*C[2] - Log[x]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-x^2*diff(y(x),x)-2*x^2*y(x) = 1+x+2*x^2*ln(x), y(x))
Maple raw output
[y(x) = exp(-x)*_C2+exp(2*x)*_C1-ln(x)]