\[ y'(x) \left (a y(x)^2+2 b x y(x)+c x^2\right )+b y(x)^2+2 c x y(x)+d x^2=0 \] ✓ Mathematica : cpu = 0.518176 (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 = 0.148 (sec), leaf count = 1388
\[\left \{y \left (x \right ) = \frac {-\frac {2 \left (a c -b^{2}\right ) c_{1}^{2} x^{2}}{\left (-4 c_{1}^{3} a^{2} d \,x^{3}+12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+4 a^{2}+4 \sqrt {c_{1}^{6} a^{2} d^{2} x^{6}-6 c_{1}^{6} a b c d \,x^{6}+4 c_{1}^{6} a \,c^{3} x^{6}+4 c_{1}^{6} b^{3} d \,x^{6}-3 c_{1}^{6} b^{2} c^{2} x^{6}-2 c_{1}^{3} a^{2} d \,x^{3}+6 c_{1}^{3} a b c \,x^{3}-4 c_{1}^{3} b^{3} x^{3}+a^{2}}\, a \right )^{\frac {1}{3}} a}-\frac {c_{1} b x}{a}+\frac {\left (-4 c_{1}^{3} a^{2} d \,x^{3}+12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+4 a^{2}+4 \sqrt {c_{1}^{6} a^{2} d^{2} x^{6}-6 c_{1}^{6} a b c d \,x^{6}+4 c_{1}^{6} a \,c^{3} x^{6}+4 c_{1}^{6} b^{3} d \,x^{6}-3 c_{1}^{6} b^{2} c^{2} x^{6}-2 c_{1}^{3} a^{2} d \,x^{3}+6 c_{1}^{3} a b c \,x^{3}-4 c_{1}^{3} b^{3} x^{3}+a^{2}}\, a \right )^{\frac {1}{3}}}{2 a}}{c_{1}}, y \left (x \right ) = -\frac {-4 \left (a c -b^{2}\right ) c_{1}^{2} x^{2}+4 c_{1} \left (12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+\left (-4 c_{1}^{3} d \,x^{3}+4\right ) a^{2}+4 \sqrt {\left (a^{2} d^{2}+4 b^{3} d -3 b^{2} c^{2}+\left (-6 b c d +4 c^{3}\right ) a \right ) c_{1}^{6} x^{6}-2 \left (a^{2} d -3 a b c +2 b^{3}\right ) c_{1}^{3} x^{3}+a^{2}}\, a \right )^{\frac {1}{3}} b x +\left (4 i \left (a c -b^{2}\right ) c_{1}^{2} x^{2}+i \left (-4 c_{1}^{3} a^{2} d \,x^{3}+12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+4 a^{2}+4 \sqrt {\left (a^{2} d^{2}+4 b^{3} d -3 b^{2} c^{2}+\left (-6 b c d +4 c^{3}\right ) a \right ) c_{1}^{6} x^{6}-2 \left (a^{2} d -3 a b c +2 b^{3}\right ) c_{1}^{3} x^{3}+a^{2}}\, a \right )^{\frac {2}{3}}\right ) \sqrt {3}+\left (-4 c_{1}^{3} a^{2} d \,x^{3}+12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+4 a^{2}+4 \sqrt {\left (a^{2} d^{2}+4 b^{3} d -3 b^{2} c^{2}+\left (-6 b c d +4 c^{3}\right ) a \right ) c_{1}^{6} x^{6}-2 \left (a^{2} d -3 a b c +2 b^{3}\right ) c_{1}^{3} x^{3}+a^{2}}\, a \right )^{\frac {2}{3}}}{4 \left (12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+\left (-4 c_{1}^{3} d \,x^{3}+4\right ) a^{2}+4 \sqrt {\left (a^{2} d^{2}+4 b^{3} d -3 b^{2} c^{2}+\left (-6 b c d +4 c^{3}\right ) a \right ) c_{1}^{6} x^{6}-2 \left (a^{2} d -3 a b c +2 b^{3}\right ) c_{1}^{3} x^{3}+a^{2}}\, a \right )^{\frac {1}{3}} c_{1} a}, y \left (x \right ) = \frac {4 \left (a c -b^{2}\right ) c_{1}^{2} x^{2}-4 c_{1} \left (12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+\left (-4 c_{1}^{3} d \,x^{3}+4\right ) a^{2}+4 \sqrt {\left (a^{2} d^{2}+4 b^{3} d -3 b^{2} c^{2}+\left (-6 b c d +4 c^{3}\right ) a \right ) c_{1}^{6} x^{6}-2 \left (a^{2} d -3 a b c +2 b^{3}\right ) c_{1}^{3} x^{3}+a^{2}}\, a \right )^{\frac {1}{3}} b x +\left (4 i \left (a c -b^{2}\right ) c_{1}^{2} x^{2}+i \left (-4 c_{1}^{3} a^{2} d \,x^{3}+12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+4 a^{2}+4 \sqrt {\left (a^{2} d^{2}+4 b^{3} d -3 b^{2} c^{2}+\left (-6 b c d +4 c^{3}\right ) a \right ) c_{1}^{6} x^{6}-2 \left (a^{2} d -3 a b c +2 b^{3}\right ) c_{1}^{3} x^{3}+a^{2}}\, a \right )^{\frac {2}{3}}\right ) \sqrt {3}-\left (-4 c_{1}^{3} a^{2} d \,x^{3}+12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+4 a^{2}+4 \sqrt {\left (a^{2} d^{2}+4 b^{3} d -3 b^{2} c^{2}+\left (-6 b c d +4 c^{3}\right ) a \right ) c_{1}^{6} x^{6}-2 \left (a^{2} d -3 a b c +2 b^{3}\right ) c_{1}^{3} x^{3}+a^{2}}\, a \right )^{\frac {2}{3}}}{4 \left (12 c_{1}^{3} a b c \,x^{3}-8 c_{1}^{3} b^{3} x^{3}+\left (-4 c_{1}^{3} d \,x^{3}+4\right ) a^{2}+4 \sqrt {\left (a^{2} d^{2}+4 b^{3} d -3 b^{2} c^{2}+\left (-6 b c d +4 c^{3}\right ) a \right ) c_{1}^{6} x^{6}-2 \left (a^{2} d -3 a b c +2 b^{3}\right ) c_{1}^{3} x^{3}+a^{2}}\, a \right )^{\frac {1}{3}} c_{1} a}\right \}\]