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 = 0.0171717 (sec), leaf count = 18
\[\left \{\left \{y(x)\to x \left (c_2 x+c_1-\sin (x)\right )\right \}\right \}\]
Maple ✓
cpu = 0.046 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) =x \left ( {\it \_C2}\,x+{\it \_C1}-\sin \left ( x \right ) \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x*(_C2*x+_C1-sin(x))