ODE
\[ a y(x)+x^6 y''(x)-x^5 y'(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0588438 (sec), leaf count = 56
\[\left \{\left \{y(x)\to \frac {1}{2} x^2 e^{-\frac {\sqrt {-a}}{2 x^2}} \left (2 c_1 e^{\frac {\sqrt {-a}}{x^2}}+\frac {c_2}{\sqrt {-a}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.047 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={x}^{2} \left ( \cosh \left ( {\frac {1}{2\,{x}^{2}}\sqrt {-a}} \right ) {\it \_C2}+\sinh \left ( {\frac {1}{2\,{x}^{2}}\sqrt {-a}} \right ) {\it \_C1} \right ) \right \} \] 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^(Sqrt[-a]/x^2)*C[1] + C[2]/Sqrt[-a]))/(2*E^(Sqrt[-a]/(2*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),'implicit')
Maple raw output
y(x) = x^2*(cosh(1/2*(-a)^(1/2)/x^2)*_C2+sinh(1/2*(-a)^(1/2)/x^2)*_C1)