ODE
\[ y(x) (a+b x)+x^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.201094 (sec), leaf count = 95
\[\left \{\left \{y(x)\to \sqrt {b} \sqrt {x} \left (c_1 \Gamma \left (1-\sqrt {1-4 a}\right ) J_{-\sqrt {1-4 a}}\left (2 \sqrt {b} \sqrt {x}\right )+c_2 \Gamma \left (\sqrt {1-4 a}+1\right ) J_{\sqrt {1-4 a}}\left (2 \sqrt {b} \sqrt {x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.023 (sec), leaf count = 47
\[\left [y \left (x \right ) = \textit {\_C1} \sqrt {x}\, \BesselJ \left (\sqrt {1-4 a}, 2 \sqrt {b}\, \sqrt {x}\right )+\textit {\_C2} \sqrt {x}\, \BesselY \left (\sqrt {1-4 a}, 2 \sqrt {b}\, \sqrt {x}\right )\right ]\] Mathematica raw input
DSolve[(a + b*x)*y[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[b]*Sqrt[x]*(BesselJ[-Sqrt[1 - 4*a], 2*Sqrt[b]*Sqrt[x]]*C[1]*Gamma[1 - Sqrt[1 - 4*a]] + BesselJ[Sqrt[1 - 4*a], 2*Sqrt[b]*Sqrt[x]]*C[2]*Gamma[1 + Sqrt[1 - 4*a]])}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+(b*x+a)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^(1/2)*BesselJ((1-4*a)^(1/2),2*b^(1/2)*x^(1/2))+_C2*x^(1/2)*BesselY((1-4*a)^(1/2),2*b^(1/2)*x^(1/2))]