ODE
\[ (a+1) y'(x)+x y''(x)-y(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0320165 (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 = 0.013 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {a}{2}}} \left ( {{\sl K}_{a}\left (2\,\sqrt {x}\right )}{\it \_C2}+{{\sl I}_{a}\left (2\,\sqrt {x}\right )}{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = x^(-1/2*a)*(BesselK(a,2*x^(1/2))*_C2+BesselI(a,2*x^(1/2))*_C1)