ODE
\[ x^2 y''(x)-(x+2) x y'(x)+(x+2) y(x)=x^3 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.157314 (sec), leaf count = 22
\[\left \{\left \{y(x)\to -x \left (x-c_2 e^x+1-c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.054 (sec), leaf count = 18
\[[y \left (x \right ) = x \textit {\_C2} +{\mathrm e}^{x} \textit {\_C1} x -x^{2}]\] Mathematica raw input
DSolve[(2 + x)*y[x] - x*(2 + x)*y'[x] + x^2*y''[x] == x^3,y[x],x]
Mathematica raw output
{{y[x] -> -(x*(1 + x - C[1] - E^x*C[2]))}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-x*(2+x)*diff(y(x),x)+(2+x)*y(x) = x^3, y(x))
Maple raw output
[y(x) = x*_C2+exp(x)*_C1*x-x^2]