\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( xy \left ( x \right ) +1 \right ) }{x \left ( -xy \left ( x \right ) -1+ \left ( y \left ( x \right ) \right ) ^{4}{x}^{3} \right ) }}=0} \]
Mathematica: cpu = 0.034004 (sec), leaf count = 2093 \[ \left \{\left \{y(x)\to \frac {c_1}{4}-\frac {1}{2} \sqrt {\frac {c_1^2}{4}+\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}+\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}}-\frac {1}{2} \sqrt {\frac {c_1^2}{2}-\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}-\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}-\frac {c_1^3-\frac {4}{x^2}}{4 \sqrt {\frac {c_1^2}{4}+\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}+\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}}}}\right \},\left \{y(x)\to \frac {c_1}{4}-\frac {1}{2} \sqrt {\frac {c_1^2}{4}+\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}+\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}}+\frac {1}{2} \sqrt {\frac {c_1^2}{2}-\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}-\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}-\frac {c_1^3-\frac {4}{x^2}}{4 \sqrt {\frac {c_1^2}{4}+\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}+\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}}}}\right \},\left \{y(x)\to \frac {c_1}{4}+\frac {1}{2} \sqrt {\frac {c_1^2}{4}+\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}+\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}}-\frac {1}{2} \sqrt {\frac {c_1^2}{2}-\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}-\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}+\frac {c_1^3-\frac {4}{x^2}}{4 \sqrt {\frac {c_1^2}{4}+\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}+\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}}}}\right \},\left \{y(x)\to \frac {c_1}{4}+\frac {1}{2} \sqrt {\frac {c_1^2}{4}+\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}+\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}}+\frac {1}{2} \sqrt {\frac {c_1^2}{2}-\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}-\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}+\frac {c_1^3-\frac {4}{x^2}}{4 \sqrt {\frac {c_1^2}{4}+\frac {\sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}{18 \sqrt [3]{2} x^3}+\frac {\sqrt [3]{2} \left (3 c_1 x^4+8 x^3\right )}{x^3 \sqrt [3]{1944 c_1^2 x^6+1458 x^5+\sqrt {\left (1944 c_1^2 x^6+1458 x^5\right ){}^2-4 \left (54 c_1 x^4+144 x^3\right ){}^3}}}}}}\right \}\right \} \]
Maple: cpu = 0.124 (sec), leaf count = 27 \[ \left \{ -{\frac {1}{2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2 }}}-{\frac {1}{3\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}}}-y \left ( x \right ) +{\it \_C1}=0 \right \} \]