\[ a x^2 y(x) y''(x)+b x^2 y'(x)^2+c x y(x) y'(x)+d y(x)^2=0 \] ✓ Mathematica : cpu = 1.55957 (sec), leaf count = 92
\[\left \{\left \{y(x)\to c_2 x^{-\frac {a \left (\sqrt {\frac {a^2-2 a (c+2 d)-4 b d+c^2}{a^2}}-1\right )+c}{2 (a+b)}} \left (x^{\sqrt {\frac {a^2-2 a (c+2 d)-4 b d+c^2}{a^2}}}+c_1\right ){}^{\frac {a}{a+b}}\right \}\right \}\]
✓ Maple : cpu = 0.342 (sec), leaf count = 136
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {1}{2\,b+2\,a}\sqrt { \left ( -4\,a-4\,b \right ) d+ \left ( a-c \right ) ^{2}}}}{x}^{{\frac {a}{2\,b+2\,a}}}{x}^{-{\frac {c}{2\,b+2\,a}}} \left ( {\frac {{a}^{2}+ \left ( -2\,c-4\,d \right ) a-4\,bd+{c}^{2}}{ \left ( a+b \right ) ^{2}} \left ( {x}^{{\frac {1}{a}\sqrt { \left ( -4\,a-4\,b \right ) d+ \left ( a-c \right ) ^{2}}}}{\it \_C1}-{\it \_C2} \right ) ^{-2}} \right ) ^{-{\frac {a}{2\,b+2\,a}}} \right \} \]