ODE
\[ a^2 y(x)+x^4 y''(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0665238 (sec), leaf count = 57
\[\left \{\left \{y(x)\to c_1 x e^{\frac {\sqrt {-a^2}}{x}}+\frac {c_2 x e^{-\frac {\sqrt {-a^2}}{x}}}{2 \sqrt {-a^2}}\right \}\right \}\]
Maple ✓
cpu = 0.033 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) =x \left ( \cos \left ( {\frac {a}{x}} \right ) {\it \_C2}+\sin \left ( {\frac {a}{x}} \right ) {\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[a^2*y[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(Sqrt[-a^2]/x)*x*C[1] + (x*C[2])/(2*Sqrt[-a^2]*E^(Sqrt[-a^2]/x))}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+a^2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x*(cos(1/x*a)*_C2+sin(1/x*a)*_C1)