ODE
\[ y(x) (a+b x)+x^2 y''(x)+x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0502349 (sec), leaf count = 80
\[\left \{\left \{y(x)\to c_1 \Gamma \left (1-2 i \sqrt {a}\right ) J_{-2 i \sqrt {a}}\left (2 \sqrt {b} \sqrt {x}\right )+c_2 \Gamma \left (2 i \sqrt {a}+1\right ) J_{2 i \sqrt {a}}\left (2 \sqrt {b} \sqrt {x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{2\,\sqrt {-a}}\left (2\,\sqrt {b}\sqrt {x}\right )}+{\it \_C2}\,{{\sl Y}_{2\,\sqrt {-a}}\left (2\,\sqrt {b}\sqrt {x}\right )} \right \} \] Mathematica raw input
DSolve[(a + b*x)*y[x] + x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> BesselJ[(-2*I)*Sqrt[a], 2*Sqrt[b]*Sqrt[x]]*C[1]*Gamma[1 - (2*I)*Sqrt[a]] + BesselJ[(2*I)*Sqrt[a], 2*Sqrt[b]*Sqrt[x]]*C[2]*Gamma[1 + (2*I)*Sqrt[a]]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)+(b*x+a)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*BesselJ(2*(-a)^(1/2),2*b^(1/2)*x^(1/2))+_C2*BesselY(2*(-a)^(1/2),2*b^(1/2)*x^(1/2))