ODE
\[ x^2 y''(x)-x y'(x)+2 y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.161561 (sec), leaf count = 20
\[\{\{y(x)\to x (c_2 \cos (\log (x))+c_1 \sin (\log (x)))\}\}\]
Maple ✓
cpu = 0.009 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} x \sin \left (\ln \left (x \right )\right )+\textit {\_C2} x \cos \left (\ln \left (x \right )\right )]\] Mathematica raw input
DSolve[2*y[x] - x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x*(C[2]*Cos[Log[x]] + C[1]*Sin[Log[x]])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x*sin(ln(x))+_C2*x*cos(ln(x))]