\[ \boxed { \left ( a \left ( y \left ( x \right ) \right ) ^{2}+2\,bxy \left ( x \right ) +c{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +b \left ( y \left ( x \right ) \right ) ^{2}+2\,cxy \left ( x \right ) +d{x}^{2}=0} \]
Mathematica: cpu = 0.056007 (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 = 0.062 (sec), leaf count = 1666 \[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( {\frac {1}{ 2\,a}\sqrt [3]{-4\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+12\,c{x}^{3}{{\it \_C1}}^{3}ba-8\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+4\,\sqrt {{{\it \_C1}}^ {6}{a}^{2}{d}^{2}{x}^{6}-6\,{{\it \_C1}}^{6}abcd{x}^{6}+4\,{{\it \_C1} }^{6}a{c}^{3}{x}^{6}+4\,{{\it \_C1}}^{6}{b}^{3}d{x}^{6}-3\,{{\it \_C1} }^{6}{b}^{2}{c}^{2}{x}^{6}-2\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+6\,c{x}^ {3}{{\it \_C1}}^{3}ba-4\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+{a}^{2}}a+4\,{ a}^{2}}}-2\,{\frac {{{\it \_C1}}^{2}{x}^{2} \left ( ac-{b}^{2} \right ) }{a\sqrt [3]{-4\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+12\,c{x}^{3}{{\it \_C1}}^{3}ba-8\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+4\,\sqrt {{{\it \_C1}}^ {6}{a}^{2}{d}^{2}{x}^{6}-6\,{{\it \_C1}}^{6}abcd{x}^{6}+4\,{{\it \_C1} }^{6}a{c}^{3}{x}^{6}+4\,{{\it \_C1}}^{6}{b}^{3}d{x}^{6}-3\,{{\it \_C1} }^{6}{b}^{2}{c}^{2}{x}^{6}-2\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+6\,c{x}^ {3}{{\it \_C1}}^{3}ba-4\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+{a}^{2}}a+4\,{ a}^{2}}}}-{\frac {bx{\it \_C1}}{a}} \right ) },y \left ( x \right ) ={ \frac {1}{{\it \_C1}} \left ( -{\frac {1}{4\,a}\sqrt [3]{-4\,{{\it \_C1 }}^{3}{a}^{2}d{x}^{3}+12\,c{x}^{3}{{\it \_C1}}^{3}ba-8\,{b}^{3}{x}^{3} {{\it \_C1}}^{3}+4\,\sqrt {{{\it \_C1}}^{6}{a}^{2}{d}^{2}{x}^{6}-6\,{{ \it \_C1}}^{6}abcd{x}^{6}+4\,{{\it \_C1}}^{6}a{c}^{3}{x}^{6}+4\,{{\it \_C1}}^{6}{b}^{3}d{x}^{6}-3\,{{\it \_C1}}^{6}{b}^{2}{c}^{2}{x}^{6}-2\, {{\it \_C1}}^{3}{a}^{2}d{x}^{3}+6\,c{x}^{3}{{\it \_C1}}^{3}ba-4\,{b}^{ 3}{x}^{3}{{\it \_C1}}^{3}+{a}^{2}}a+4\,{a}^{2}}}+{\frac {{{\it \_C1}}^ {2}{x}^{2} \left ( ac-{b}^{2} \right ) }{a}{\frac {1}{\sqrt [3]{-4\,{{ \it \_C1}}^{3}{a}^{2}d{x}^{3}+12\,c{x}^{3}{{\it \_C1}}^{3}ba-8\,{b}^{3 }{x}^{3}{{\it \_C1}}^{3}+4\,\sqrt {{{\it \_C1}}^{6}{a}^{2}{d}^{2}{x}^{ 6}-6\,{{\it \_C1}}^{6}abcd{x}^{6}+4\,{{\it \_C1}}^{6}a{c}^{3}{x}^{6}+4 \,{{\it \_C1}}^{6}{b}^{3}d{x}^{6}-3\,{{\it \_C1}}^{6}{b}^{2}{c}^{2}{x} ^{6}-2\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+6\,c{x}^{3}{{\it \_C1}}^{3}ba- 4\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+{a}^{2}}a+4\,{a}^{2}}}}}-{\frac {bx{ \it \_C1}}{a}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{2\,a}\sqrt [3 ]{-4\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+12\,c{x}^{3}{{\it \_C1}}^{3}ba-8 \,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+4\,\sqrt {{{\it \_C1}}^{6}{a}^{2}{d}^ {2}{x}^{6}-6\,{{\it \_C1}}^{6}abcd{x}^{6}+4\,{{\it \_C1}}^{6}a{c}^{3}{ x}^{6}+4\,{{\it \_C1}}^{6}{b}^{3}d{x}^{6}-3\,{{\it \_C1}}^{6}{b}^{2}{c }^{2}{x}^{6}-2\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+6\,c{x}^{3}{{\it \_C1} }^{3}ba-4\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+{a}^{2}}a+4\,{a}^{2}}}+2\,{ \frac {{{\it \_C1}}^{2}{x}^{2} \left ( ac-{b}^{2} \right ) }{a\sqrt [3]{ -4\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+12\,c{x}^{3}{{\it \_C1}}^{3}ba-8\, {b}^{3}{x}^{3}{{\it \_C1}}^{3}+4\,\sqrt {{{\it \_C1}}^{6}{a}^{2}{d}^{2 }{x}^{6}-6\,{{\it \_C1}}^{6}abcd{x}^{6}+4\,{{\it \_C1}}^{6}a{c}^{3}{x} ^{6}+4\,{{\it \_C1}}^{6}{b}^{3}d{x}^{6}-3\,{{\it \_C1}}^{6}{b}^{2}{c}^ {2}{x}^{6}-2\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+6\,c{x}^{3}{{\it \_C1}}^ {3}ba-4\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+{a}^{2}}a+4\,{a}^{2}}}} \right ) \right ) },y \left ( x \right ) ={\frac {1}{{\it \_C1}} \left ( -{\frac {1}{4\,a}\sqrt [3]{-4\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+12\,c{x }^{3}{{\it \_C1}}^{3}ba-8\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+4\,\sqrt {{{ \it \_C1}}^{6}{a}^{2}{d}^{2}{x}^{6}-6\,{{\it \_C1}}^{6}abcd{x}^{6}+4\, {{\it \_C1}}^{6}a{c}^{3}{x}^{6}+4\,{{\it \_C1}}^{6}{b}^{3}d{x}^{6}-3\, {{\it \_C1}}^{6}{b}^{2}{c}^{2}{x}^{6}-2\,{{\it \_C1}}^{3}{a}^{2}d{x}^{ 3}+6\,c{x}^{3}{{\it \_C1}}^{3}ba-4\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+{a} ^{2}}a+4\,{a}^{2}}}+{\frac {{{\it \_C1}}^{2}{x}^{2} \left ( ac-{b}^{2} \right ) }{a}{\frac {1}{\sqrt [3]{-4\,{{\it \_C1}}^{3}{a}^{2}d{x}^{3}+ 12\,c{x}^{3}{{\it \_C1}}^{3}ba-8\,{b}^{3}{x}^{3}{{\it \_C1}}^{3}+4\, \sqrt {{{\it \_C1}}^{6}{a}^{2}{d}^{2}{x}^{6}-6\,{{\it \_C1}}^{6}abcd{x }^{6}+4\,{{\it \_C1}}^{6}a{c}^{3}{x}^{6}+4\,{{\it \_C1}}^{6}{b}^{3}d{x }^{6}-3\,{{\it \_C1}}^{6}{b}^{2}{c}^{2}{x}^{6}-2\,{{\it \_C1}}^{3}{a}^ {2}d{x}^{3}+6\,c{x}^{3}{{\it \_C1}}^{3}ba-4\,{b}^{3}{x}^{3}{{\it \_C1} }^{3}+{a}^{2}}a+4\,{a}^{2}}}}}-{\frac {bx{\it \_C1}}{a}}+{\frac {i}{2} }\sqrt {3} \left ( {\frac {1}{2\,a}\sqrt [3]{-4\,{{\it \_C1}}^{3}{a}^{2 }d{x}^{3}+12\,c{x}^{3}{{\it \_C1}}^{3}ba-8\,{b}^{3}{x}^{3}{{\it \_C1}} ^{3}+4\,\sqrt {{{\it \_C1}}^{6}{a}^{2}{d}^{2}{x}^{6}-6\,{{\it \_C1}}^{ 6}abcd{x}^{6}+4\,{{\it \_C1}}^{6}a{c}^{3}{x}^{6}+4\,{{\it \_C1}}^{6}{b }^{3}d{x}^{6}-3\,{{\it \_C1}}^{6}{b}^{2}{c}^{2}{x}^{6}-2\,{{\it \_C1}} ^{3}{a}^{2}d{x}^{3}+6\,c{x}^{3}{{\it \_C1}}^{3}ba-4\,{b}^{3}{x}^{3}{{ \it \_C1}}^{3}+{a}^{2}}a+4\,{a}^{2}}}+2\,{\frac {{{\it \_C1}}^{2}{x}^{ 2} \left ( ac-{b}^{2} \right ) }{a\sqrt [3]{-4\,{{\it \_C1}}^{3}{a}^{2}d {x}^{3}+12\,c{x}^{3}{{\it \_C1}}^{3}ba-8\,{b}^{3}{x}^{3}{{\it \_C1}}^{ 3}+4\,\sqrt {{{\it \_C1}}^{6}{a}^{2}{d}^{2}{x}^{6}-6\,{{\it \_C1}}^{6} abcd{x}^{6}+4\,{{\it \_C1}}^{6}a{c}^{3}{x}^{6}+4\,{{\it \_C1}}^{6}{b}^ {3}d{x}^{6}-3\,{{\it \_C1}}^{6}{b}^{2}{c}^{2}{x}^{6}-2\,{{\it \_C1}}^{ 3}{a}^{2}d{x}^{3}+6\,c{x}^{3}{{\it \_C1}}^{3}ba-4\,{b}^{3}{x}^{3}{{ \it \_C1}}^{3}+{a}^{2}}a+4\,{a}^{2}}}} \right ) \right ) } \right \} \]