\[ a x^2 y(x) y''(x)+b x^2 y'(x)^2+c x y(x) y'(x)+d y(x)^2=0 \] ✓ Mathematica : cpu = 1.29556 (sec), leaf count = 93
\[\left \{\left \{y(x)\to c_2 \exp \left (-\frac {\log (x) \left (a \sqrt {\frac {a^2-2 a c-4 a d-4 b d+c^2}{a^2}}-a+c\right )-2 a \log \left (x^{\sqrt {\frac {a^2-2 a c-4 a d-4 b d+c^2}{a^2}}}+c_1\right )}{2 (a+b)}\right )\right \}\right \}\]
✓ Maple : cpu = 0.252 (sec), leaf count = 155
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {1}{2\,a+2\,b}\sqrt {{a}^{2}-2\,ca-4\,da-4\,db+{c}^{2}}}}{x}^{{\frac {a}{2\,a+2\,b}}}{x}^{-{\frac {c}{2\,a+2\,b}}} \left ( {({a}^{2}-2\,ca-4\,da-4\,db+{c}^{2}) \left ( {x}^{{\frac {1}{a}\sqrt {{a}^{2}-2\,ca-4\,da-4\,db+{c}^{2}}}}{\it \_C1}\,a+{x}^{{\frac {1}{a}\sqrt {{a}^{2}-2\,ca-4\,da-4\,db+{c}^{2}}}}{\it \_C1}\,b-{\it \_C2}\,a-{\it \_C2}\,b \right ) ^{-2}} \right ) ^{-{\frac {a}{2\,a+2\,b}}} \right \} \]