ODE
\[ a y(x)+x^6 y''(x)-x^5 y'(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.25576 (sec), leaf count = 58
\[\left \{\left \{y(x)\to \frac {1}{2} x^2 e^{-\frac {i \sqrt {a}}{2 x^2}} \left (2 c_1 e^{\frac {i \sqrt {a}}{x^2}}-\frac {i c_2}{\sqrt {a}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.108 (sec), leaf count = 37
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{2} \sinh \left (\frac {\sqrt {-a}}{2 x^{2}}\right )+\textit {\_C2} \,x^{2} \cosh \left (\frac {\sqrt {-a}}{2 x^{2}}\right )\right ]\] Mathematica raw input
DSolve[a*y[x] - x^5*y'[x] + x^6*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^2*(2*E^((I*Sqrt[a])/x^2)*C[1] - (I*C[2])/Sqrt[a]))/(2*E^(((I/2)*Sqrt[a])/x^2))}}
Maple raw input
dsolve(x^6*diff(diff(y(x),x),x)-x^5*diff(y(x),x)+a*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^2*sinh(1/2*(-a)^(1/2)/x^2)+_C2*x^2*cosh(1/2*(-a)^(1/2)/x^2)]