ODE
\[ (a+1) y'(x)+x y''(x)-y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.180267 (sec), leaf count = 58
\[\left \{\left \{y(x)\to (-1)^{-a} x^{-a/2} \left (c_2 \Gamma (1-a) I_{-a}\left (2 \sqrt {x}\right )+(-1)^a c_1 \Gamma (a+1) I_a\left (2 \sqrt {x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 33
\[\left [y \left (x \right ) = \textit {\_C1} \,x^{-\frac {a}{2}} \BesselI \left (a , 2 \sqrt {x}\right )+\textit {\_C2} \,x^{-\frac {a}{2}} \BesselK \left (a , 2 \sqrt {x}\right )\right ]\] Mathematica raw input
DSolve[-y[x] + (1 + a)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (BesselI[-a, 2*Sqrt[x]]*C[2]*Gamma[1 - a] + (-1)^a*BesselI[a, 2*Sqrt[x]]*C[1]*Gamma[1 + a])/((-1)^a*x^(a/2))}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+(1+a)*diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(-1/2*a)*BesselI(a,2*x^(1/2))+_C2*x^(-1/2*a)*BesselK(a,2*x^(1/2))]