\[ \left (3 x y(x)^3-4 x y(x)+y(x)\right ) y'(x)+\left (y(x)^2-2\right ) y(x)^2=0 \] ✓ Mathematica : cpu = 0.144994 (sec), leaf count = 2353
\[\left \{\{y(x)\to 0\},\left \{y(x)\to -\frac {\sqrt {\frac {8 \sqrt [3]{2} x^4+8 \sqrt [3]{2} x^3+2 \left (2 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}+\sqrt [3]{2}\right ) x^2-4 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}} x+\left (32 x^6+48 x^5-6 \left (9 c_1^2-4\right ) x^4+4 x^3+6 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}\right ){}^{2/3}}{x^2 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}}}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {\frac {8 \sqrt [3]{2} x^4+8 \sqrt [3]{2} x^3+2 \left (2 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}+\sqrt [3]{2}\right ) x^2-4 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}} x+\left (32 x^6+48 x^5-6 \left (9 c_1^2-4\right ) x^4+4 x^3+6 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}\right ){}^{2/3}}{x^2 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}}}}{\sqrt {6}}\right \},\left \{y(x)\to -\frac {\sqrt {\frac {8 i \sqrt [3]{2} \left (i+\sqrt {3}\right ) x^4+8 i \sqrt [3]{2} \left (i+\sqrt {3}\right ) x^3+2 \left (4 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}+i \sqrt [3]{2} \sqrt {3}-\sqrt [3]{2}\right ) x^2-8 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}} x-i \left (-i+\sqrt {3}\right ) \left (32 x^6+48 x^5-6 \left (9 c_1^2-4\right ) x^4+4 x^3+6 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}\right ){}^{2/3}}{x^2 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}}}}{2 \sqrt {3}}\right \},\left \{y(x)\to \frac {\sqrt {\frac {8 i \sqrt [3]{2} \left (i+\sqrt {3}\right ) x^4+8 i \sqrt [3]{2} \left (i+\sqrt {3}\right ) x^3+2 \left (4 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}+i \sqrt [3]{2} \sqrt {3}-\sqrt [3]{2}\right ) x^2-8 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}} x-i \left (-i+\sqrt {3}\right ) \left (32 x^6+48 x^5-6 \left (9 c_1^2-4\right ) x^4+4 x^3+6 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}\right ){}^{2/3}}{x^2 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}}}}{2 \sqrt {3}}\right \},\left \{y(x)\to -\frac {\sqrt {\frac {-8 i \sqrt [3]{2} \left (-i+\sqrt {3}\right ) x^4-8 i \sqrt [3]{2} \left (-i+\sqrt {3}\right ) x^3+2 \left (4 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}-i \sqrt [3]{2} \sqrt {3}-\sqrt [3]{2}\right ) x^2-8 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}} x+i \left (i+\sqrt {3}\right ) \left (32 x^6+48 x^5-6 \left (9 c_1^2-4\right ) x^4+4 x^3+6 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}\right ){}^{2/3}}{x^2 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}}}}{2 \sqrt {3}}\right \},\left \{y(x)\to \frac {\sqrt {\frac {-8 i \sqrt [3]{2} \left (-i+\sqrt {3}\right ) x^4-8 i \sqrt [3]{2} \left (-i+\sqrt {3}\right ) x^3+2 \left (4 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}-i \sqrt [3]{2} \sqrt {3}-\sqrt [3]{2}\right ) x^2-8 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}} x+i \left (i+\sqrt {3}\right ) \left (32 x^6+48 x^5-6 \left (9 c_1^2-4\right ) x^4+4 x^3+6 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}\right ){}^{2/3}}{x^2 \sqrt [3]{16 x^6+24 x^5-3 \left (9 c_1^2-4\right ) x^4+2 x^3+3 \sqrt {3} \sqrt {-x^7 c_1^2 \left (32 x^3+48 x^2-27 c_1^2 x+24 x+4\right )}}}}}{2 \sqrt {3}}\right \}\right \}\]
✓ Maple : cpu = 0.022 (sec), leaf count = 28
\[ \left \{ x+ \left ( y \left ( x \right ) \right ) ^{-2}-{\frac {{\it \_C1}}{ \left ( y \left ( x \right ) \right ) ^{2}}{\frac {1}{\sqrt { \left ( y \left ( x \right ) \right ) ^{2}-2}}}}=0,y \left ( x \right ) =0 \right \} \]