2.309   ODE No. 309

\[ -2 x^3+\left (2 y(x)^3+y(x)\right ) y'(x)-x=0 \]

✓ Mathematica : cpu = 0.0801192 (sec), leaf count = 151

DSolve[-x - 2*x^3 + (y[x] + 2*y[x]^3)*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {\sqrt {-1-\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-1-\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {-1+\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-1+\sqrt {4 x^4+4 x^2+1+8 c_1}}}{\sqrt {2}}\right \}\right \}\]

✓ Maple : cpu = 0.052 (sec), leaf count = 113

dsolve((2*y(x)^3+y(x))*diff(y(x),x)-2*x^3-x = 0,y(x))
 

\[y \left (x \right ) = -\frac {\sqrt {-2-2 \sqrt {4 x^{4}+4 x^{2}+8 c_{1} +1}}}{2}\]