\[ y'(x)=\frac {y(x) (x y(x)+1)}{x \left (x^3 y(x)^4-x y(x)-1\right )} \] ✓ Mathematica : cpu = 0.216683 (sec), leaf count = 2093
DSolve[Derivative[1][y][x] == (y[x]*(1 + x*y[x]))/(x*(-1 - x*y[x] + x^3*y[x]^4)),y[x],x]
\[\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 = 0.134 (sec), leaf count = 27
dsolve(diff(y(x),x) = 1/x*y(x)*(x*y(x)+1)/(-x*y(x)-1+y(x)^4*x^3),y(x))
\[-\frac {1}{2 x^{2} y \left (x \right )^{2}}-\frac {1}{3 y \left (x \right )^{3} x^{3}}-y \left (x \right )+c_{1} = 0\]