ODE
\[ -a^2 x^3 y(x)+x y''(x)-y'(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.159099 (sec), leaf count = 33
\[\left \{\left \{y(x)\to c_1 \cosh \left (\frac {a x^2}{2}\right )+i c_2 \sinh \left (\frac {a x^2}{2}\right )\right \}\right \}\]
Maple ✓
cpu = 0.039 (sec), leaf count = 23
\[\left [y \left (x \right ) = \textit {\_C1} \sinh \left (\frac {a \,x^{2}}{2}\right )+\textit {\_C2} \cosh \left (\frac {a \,x^{2}}{2}\right )\right ]\] Mathematica raw input
DSolve[-(a^2*x^3*y[x]) - y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cosh[(a*x^2)/2] + I*C[2]*Sinh[(a*x^2)/2]}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-diff(y(x),x)-a^2*x^3*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*sinh(1/2*a*x^2)+_C2*cosh(1/2*a*x^2)]