\[ y(x) \left (y(x)^3-2 x^3\right ) y'(x)+x \left (2 y(x)^3-x^3\right )=0 \] ✓ Mathematica : cpu = 0.194464 (sec), leaf count = 139
DSolve[x*(-x^3 + 2*y[x]^3) + y[x]*(-2*x^3 + y[x]^3)*Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [\frac {1}{7} \text {RootSum}\left [\text {$\#$1}^4+\text {$\#$1}^3+3 \text {$\#$1}^2+\text {$\#$1}+1\& ,\frac {8 \text {$\#$1}^3 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+9 \text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+12 \text {$\#$1} \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )-\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{4 \text {$\#$1}^3+3 \text {$\#$1}^2+6 \text {$\#$1}+1}\& \right ]-\frac {1}{7} \log \left (1-\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.669 (sec), leaf count = 124
dsolve(y(x)*(y(x)^3-2*x^3)*diff(y(x),x)+(2*y(x)^3-x^3)*x = 0,y(x))
\[\frac {\ln \left (\frac {y \left (x \right )-x}{x}\right )}{7}-\frac {2 \ln \left (\frac {4 x^{4}+4 x^{3} y \left (x \right )+12 x^{2} y \left (x \right )^{2}+4 x y \left (x \right )^{3}+4 y \left (x \right )^{4}}{x^{4}}\right )}{7}-\frac {2 \sqrt {3}\, \arctan \left (\frac {\left (x +2 y \left (x \right )\right ) \sqrt {3}}{3 x}\right )}{7}+\frac {2 \sqrt {3}\, \arctan \left (\frac {\sqrt {3}\, \left (x^{3}+4 x^{2} y \left (x \right )+2 x y \left (x \right )^{2}+2 y \left (x \right )^{3}\right )}{3 x^{3}}\right )}{7}-\ln \left (x \right )-c_{1} = 0\]