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 = 0.0164543 (sec), leaf count = 22
\[\left \{\left \{y(x)\to -x \left (-c_2 e^x-c_1+x+1\right )\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) =x \left ( {{\rm e}^{x}}{\it \_C1}+{\it \_C2}-x \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x*(exp(x)*_C1+_C2-x)