ODE
\[ a y'(x)+b y(x)+x y''(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0532441 (sec), leaf count = 77
\[\left \{\left \{y(x)\to b^{\frac {1}{2}-\frac {a}{2}} x^{\frac {1}{2}-\frac {a}{2}} \left (c_2 \Gamma (2-a) J_{1-a}\left (2 \sqrt {b} \sqrt {x}\right )+c_1 \Gamma (a) J_{a-1}\left (2 \sqrt {b} \sqrt {x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {a}{2}}+{\frac {1}{2}}} \left ( {{\sl Y}_{a-1}\left (2\,\sqrt {b}\sqrt {x}\right )}{\it \_C2}+{{\sl J}_{a-1}\left (2\,\sqrt {b}\sqrt {x}\right )}{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[b*y[x] + a*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> b^(1/2 - a/2)*x^(1/2 - a/2)*(BesselJ[1 - a, 2*Sqrt[b]*Sqrt[x]]*C[2]*Gamma[2 - a] + BesselJ[-1 + a, 2*Sqrt[b]*Sqrt[x]]*C[1]*Gamma[a])}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+a*diff(y(x),x)+b*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^(-1/2*a+1/2)*(BesselY(a-1,2*b^(1/2)*x^(1/2))*_C2+BesselJ(a-1,2*b^(1/2)*x^(1/2))*_C1)