ODE
\[ 2 n y'(x)+x y''(x)-y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.17879 (sec), leaf count = 69
\[\left \{\left \{y(x)\to (-1)^{-2 n} x^{\frac {1}{2}-n} \left (c_1 (-1)^{2 n} \Gamma (2 n) I_{2 n-1}\left (2 \sqrt {x}\right )-c_2 \Gamma (2-2 n) I_{1-2 n}\left (2 \sqrt {x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.032 (sec), leaf count = 45
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{-n +\frac {1}{2}} \BesselI \left (2 n -1, 2 \sqrt {x}\right )+\textit {\_C2} \,x^{-n +\frac {1}{2}} \BesselK \left (2 n -1, 2 \sqrt {x}\right )\right ]\] Mathematica raw input
DSolve[-y[x] + 2*n*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (x^(1/2 - n)*(-(BesselI[1 - 2*n, 2*Sqrt[x]]*C[2]*Gamma[2 - 2*n]) + (-1)^(2*n)*BesselI[-1 + 2*n, 2*Sqrt[x]]*C[1]*Gamma[2*n]))/(-1)^(2*n)}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+2*n*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(-n+1/2)*BesselI(2*n-1,2*x^(1/2))+_C2*x^(-n+1/2)*BesselK(2*n-1,2*x^(1/2))]