ODE
\[ a^2 y(x)+x^4 y''(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.314472 (sec), leaf count = 42
\[\left \{\left \{y(x)\to c_1 x e^{\frac {i a}{x}}-\frac {i c_2 x e^{-\frac {i a}{x}}}{2 a}\right \}\right \}\]
Maple ✓
cpu = 0.099 (sec), leaf count = 23
\[\left [y \left (x \right ) = \textit {\_C1} x \sin \left (\frac {a}{x}\right )+\textit {\_C2} x \cos \left (\frac {a}{x}\right )\right ]\] Mathematica raw input
DSolve[a^2*y[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^((I*a)/x)*x*C[1] - ((I/2)*x*C[2])/(a*E^((I*a)/x))}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+a^2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x*sin(a/x)+_C2*x*cos(a/x)]