ODE
\[ x^2 y''(x)-2 x y'(x)+2 y(x)=4 x^3 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0124222 (sec), leaf count = 19
\[\left \{\left \{y(x)\to x \left (c_2 x+c_1+2 x^2\right )\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={x}^{2}{\it \_C2}+2\,{x}^{3}+{\it \_C1}\,x \right \} \] Mathematica raw input
DSolve[2*y[x] - 2*x*y'[x] + x^2*y''[x] == 4*x^3,y[x],x]
Mathematica raw output
{{y[x] -> x*(2*x^2 + C[1] + x*C[2])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x) = 4*x^3, y(x),'implicit')
Maple raw output
y(x) = _C2*x^2+2*x^3+_C1*x