ODE
\[ x^2 y''(x)-2 x y'(x)+2 y(x)=x^3 \sin (x) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.165049 (sec), leaf count = 18
\[\{\{y(x)\to x (-\sin (x)+c_2 x+c_1)\}\}\]
Maple ✓
cpu = 0.169 (sec), leaf count = 18
\[[y \left (x \right ) = x^{2} \textit {\_C2} +\textit {\_C1} x -x \sin \left (x \right )]\] Mathematica raw input
DSolve[2*y[x] - 2*x*y'[x] + x^2*y''[x] == x^3*Sin[x],y[x],x]
Mathematica raw output
{{y[x] -> x*(C[1] + x*C[2] - Sin[x])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x) = x^3*sin(x), y(x))
Maple raw output
[y(x) = x^2*_C2+_C1*x-x*sin(x)]