\[ y'(x) \left (a y(x)^2+2 b x y(x)+c x^2\right )+b y(x)^2+2 c x y(x)+d x^2=0 \] ✓ Mathematica : cpu = 0.458174 (sec), leaf count = 831
\[\left \{\left \{y(x)\to -\frac {b x}{a}+\frac {\sqrt [3]{-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}+\sqrt {4 \left (9 a c x^2-9 b^2 x^2\right )^3+\left (-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}\right ){}^2}}}{3 \sqrt [3]{2} a}-\frac {\sqrt [3]{2} \left (9 a c x^2-9 b^2 x^2\right )}{3 a \sqrt [3]{-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}+\sqrt {4 \left (9 a c x^2-9 b^2 x^2\right )^3+\left (-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}\right ){}^2}}}\right \},\left \{y(x)\to -\frac {b x}{a}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}+\sqrt {4 \left (9 a c x^2-9 b^2 x^2\right )^3+\left (-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}\right ){}^2}}}{6 \sqrt [3]{2} a}+\frac {\left (1+i \sqrt {3}\right ) \left (9 a c x^2-9 b^2 x^2\right )}{3\ 2^{2/3} a \sqrt [3]{-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}+\sqrt {4 \left (9 a c x^2-9 b^2 x^2\right )^3+\left (-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}\right ){}^2}}}\right \},\left \{y(x)\to -\frac {b x}{a}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}+\sqrt {4 \left (9 a c x^2-9 b^2 x^2\right )^3+\left (-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}\right ){}^2}}}{6 \sqrt [3]{2} a}+\frac {\left (1-i \sqrt {3}\right ) \left (9 a c x^2-9 b^2 x^2\right )}{3\ 2^{2/3} a \sqrt [3]{-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}+\sqrt {4 \left (9 a c x^2-9 b^2 x^2\right )^3+\left (-54 b^3 x^3+81 a b c x^3-27 a^2 d x^3+27 a^2 e^{3 c_1}\right ){}^2}}}\right \}\right \}\] ✓ Maple : cpu = 0.132 (sec), leaf count = 1388
\[y \relax (x ) = \frac {\frac {\left (-4 c_{1}^{3} a^{2} d \,x^{3}+12 c \,x^{3} c_{1}^{3} b a -8 b^{3} x^{3} c_{1}^{3}+4 \sqrt {a^{2} d^{2} x^{6} c_{1}^{6}-6 a b c d \,x^{6} c_{1}^{6}+4 a \,c^{3} x^{6} c_{1}^{6}+4 b^{3} d \,x^{6} c_{1}^{6}-3 b^{2} c^{2} x^{6} c_{1}^{6}-2 c_{1}^{3} a^{2} d \,x^{3}+6 c \,x^{3} c_{1}^{3} b a -4 b^{3} x^{3} c_{1}^{3}+a^{2}}\, a +4 a^{2}\right )^{\frac {1}{3}}}{2 a}-\frac {2 c_{1}^{2} x^{2} \left (a c -b^{2}\right )}{a \left (-4 c_{1}^{3} a^{2} d \,x^{3}+12 c \,x^{3} c_{1}^{3} b a -8 b^{3} x^{3} c_{1}^{3}+4 \sqrt {a^{2} d^{2} x^{6} c_{1}^{6}-6 a b c d \,x^{6} c_{1}^{6}+4 a \,c^{3} x^{6} c_{1}^{6}+4 b^{3} d \,x^{6} c_{1}^{6}-3 b^{2} c^{2} x^{6} c_{1}^{6}-2 c_{1}^{3} a^{2} d \,x^{3}+6 c \,x^{3} c_{1}^{3} b a -4 b^{3} x^{3} c_{1}^{3}+a^{2}}\, a +4 a^{2}\right )^{\frac {1}{3}}}-\frac {b x c_{1}}{a}}{c_{1}}\]