\[ a x y''(x)+b y'(x)+c y(x)=0 \] ✓ Mathematica : cpu = 0.0351387 (sec), leaf count = 190
DSolve[c*y[x] + b*Derivative[1][y][x] + a*x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 a^{\frac {1}{2} \left (\frac {b}{a}-1\right )} c^{\frac {1}{2} \left (1-\frac {b}{a}\right )} x^{\frac {1}{2} \left (1-\frac {b}{a}\right )} \Gamma \left (\frac {b}{a}\right ) J_{\frac {b}{a}-1}\left (\frac {2 \sqrt {c} \sqrt {x}}{\sqrt {a}}\right )+c_2 a^{\frac {1}{2} \left (1-\frac {b}{a}\right )-\frac {a-b}{a}} c^{\frac {a-b}{a}+\frac {1}{2} \left (\frac {b}{a}-1\right )} x^{\frac {a-b}{a}+\frac {1}{2} \left (\frac {b}{a}-1\right )} \Gamma \left (2-\frac {b}{a}\right ) J_{1-\frac {b}{a}}\left (\frac {2 \sqrt {c} \sqrt {x}}{\sqrt {a}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.021 (sec), leaf count = 66
dsolve(a*x*diff(diff(y(x),x),x)+b*diff(y(x),x)+c*y(x)=0,y(x))
\[y \left (x \right ) = x^{\frac {a -b}{2 a}} \left (\BesselY \left (\frac {-a +b}{a}, 2 \sqrt {\frac {c}{a}}\, \sqrt {x}\right ) c_{2}+\BesselJ \left (\frac {-a +b}{a}, 2 \sqrt {\frac {c}{a}}\, \sqrt {x}\right ) c_{1}\right )\]