ODE
\[ x \left (2-x^2\right ) y''(x)-\left (\left (x^2+4 x+2\right ) y(x)\right )-\left (-x^3-3 x^2+2 x+2\right ) y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.228544 (sec), leaf count = 21
\[\left \{\left \{y(x)\to c_1 e^x x^2+c_2 (x-1)\right \}\right \}\]
Maple ✓
cpu = 0.075 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} \left (x -1\right )+\textit {\_C2} \,x^{2} {\mathrm e}^{x}]\] Mathematica raw input
DSolve[-((2 + 4*x + x^2)*y[x]) - (2 + 2*x - 3*x^2 - x^3)*y'[x] + x*(2 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*x^2*C[1] + (-1 + x)*C[2]}}
Maple raw input
dsolve(x*(-x^2+2)*diff(diff(y(x),x),x)-(-x^3-3*x^2+2*x+2)*diff(y(x),x)-(x^2+4*x+2)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*(x-1)+_C2*x^2*exp(x)]