ODE
\[ a^2 (-y(x))+x^2 y''(x)+x y'(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.163936 (sec), leaf count = 25
\[\{\{y(x)\to c_1 \cosh (a \log (x))+i c_2 \sinh (a \log (x))\}\}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} \,x^{a}+\textit {\_C2} \,x^{-a}]\] Mathematica raw input
DSolve[-(a^2*y[x]) + x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cosh[a*Log[x]] + I*C[2]*Sinh[a*Log[x]]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-a^2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^a+_C2*x^(-a)]