ODE
\[ x^2 y''(x)-2 x y'(x)+2 y(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.159938 (sec), leaf count = 14
\[\{\{y(x)\to x (c_2 x+c_1)\}\}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 13
\[[y \left (x \right ) = x^{2} \textit {\_C1} +\textit {\_C2} x]\] Mathematica raw input
DSolve[2*y[x] - 2*x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(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) = 0, y(x))
Maple raw output
[y(x) = _C1*x^2+_C2*x]