\[ \left (2 x^3 y(x)^3-x\right ) y'(x)+2 x^3 y(x)^3-y(x)=0 \] ✓ Mathematica : cpu = 0.121467 (sec), leaf count = 723
DSolve[-y[x] + 2*x^3*y[x]^3 + (-x + 2*x^3*y[x]^3)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {2 x^3-c_1 x^2}{6 x^2}+\frac {\sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {16 x^{13}-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}+27 x^8}}}{6 x^2}+\frac {\left (2 x^3-c_1 x^2\right ){}^2}{6 x^2 \sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {16 x^{13}-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}+27 x^8}}}\right \},\left \{y(x)\to -\frac {2 x^3-c_1 x^2}{6 x^2}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {16 x^{13}-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}+27 x^8}}}{12 x^2}-\frac {\left (1+i \sqrt {3}\right ) \left (2 x^3-c_1 x^2\right ){}^2}{12 x^2 \sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {16 x^{13}-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}+27 x^8}}}\right \},\left \{y(x)\to -\frac {2 x^3-c_1 x^2}{6 x^2}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {16 x^{13}-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}+27 x^8}}}{12 x^2}-\frac {\left (1-i \sqrt {3}\right ) \left (2 x^3-c_1 x^2\right ){}^2}{12 x^2 \sqrt [3]{-8 x^9+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6-27 x^4+3 \sqrt {3} \sqrt {16 x^{13}-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}+27 x^8}}}\right \}\right \}\] ✓ Maple : cpu = 0.129 (sec), leaf count = 815
dsolve((2*x^3*y(x)^3-x)*diff(y(x),x)+2*x^3*y(x)^3-y(x) = 0,y(x))
\[y \left (x \right ) = \frac {\left (\left (x^{2} c_{1}^{3}-6 c_{1}^{2} x^{3}+12 c_{1} x^{4}-8 x^{5}+3 \sqrt {48 x^{5}-72 c_{1} x^{4}+36 c_{1}^{2} x^{3}-6 x^{2} c_{1}^{3}+81}-27\right ) x \right )^{\frac {1}{3}}}{6 x}+\frac {\left (c_{1}-2 x \right )^{2} x}{6 \left (\left (x^{2} c_{1}^{3}-6 c_{1}^{2} x^{3}+12 c_{1} x^{4}-8 x^{5}+3 \sqrt {48 x^{5}-72 c_{1} x^{4}+36 c_{1}^{2} x^{3}-6 x^{2} c_{1}^{3}+81}-27\right ) x \right )^{\frac {1}{3}}}+\frac {c_{1}}{6}-\frac {x}{3}\]