ODE
\[ a^2 y(x)+x^4 y''(x)+2 x^3 y'(x)=0 \] ODE Classification
[[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.163919 (sec), leaf count = 25
\[\left \{\left \{y(x)\to c_1 \cos \left (\frac {a}{x}\right )-c_2 \sin \left (\frac {a}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.056 (sec), leaf count = 21
\[\left [y \left (x \right ) = \textit {\_C1} \sin \left (\frac {a}{x}\right )+\textit {\_C2} \cos \left (\frac {a}{x}\right )\right ]\] Mathematica raw input
DSolve[a^2*y[x] + 2*x^3*y'[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cos[a/x] - C[2]*Sin[a/x]}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+2*x^3*diff(y(x),x)+a^2*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*sin(a/x)+_C2*cos(a/x)]