ODE
\[ x^4 y''(x)+x^3 y'(x)+y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.167661 (sec), leaf count = 31
\[\left \{\left \{y(x)\to c_2 J_0\left (\frac {1}{x}\right )+\frac {c_1 K_0\left (\frac {i}{x}\right )}{\sqrt {\pi }}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{0}\left ({x}^{-1}\right )}+{\it \_C2}\,{{\sl Y}_{0}\left ({x}^{-1}\right )} \right \} \] Mathematica raw input
DSolve[y[x] + x^3*y'[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (BesselK[0, I/x]*C[1])/Sqrt[Pi] + BesselJ[0, x^(-1)]*C[2]}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+x^3*diff(y(x),x)+y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*BesselJ(0,1/x)+_C2*BesselY(0,1/x)