\[ y(x) \left (a b x+c x^2+d\right )+x (2 a x+b) y'(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0693041 (sec), leaf count = 120
DSolve[(d + a*b*x + c*x^2)*y[x] + x*(b + 2*a*x)*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} (-2 a x-(b-1) \log (x))} J_{\frac {1}{2} \sqrt {b^2-2 b-4 d+1}}\left (-i \sqrt {a^2-c} x\right )+c_2 e^{\frac {1}{2} (-2 a x-(b-1) \log (x))} Y_{\frac {1}{2} \sqrt {b^2-2 b-4 d+1}}\left (-i \sqrt {a^2-c} x\right )\right \}\right \}\] ✓ Maple : cpu = 0.07 (sec), leaf count = 76
dsolve(x^2*diff(diff(y(x),x),x)+(2*a*x+b)*x*diff(y(x),x)+(a*b*x+c*x^2+d)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-a x} x^{-\frac {b}{2}+\frac {1}{2}} \left (\BesselY \left (\frac {\sqrt {b^{2}-2 b -4 d +1}}{2}, \sqrt {-a^{2}+c}\, x \right ) c_{2}+\BesselJ \left (\frac {\sqrt {b^{2}-2 b -4 d +1}}{2}, \sqrt {-a^{2}+c}\, x \right ) c_{1}\right )\]