2.320   ODE No. 320

\[ \left (x^2 y(x)^3+x y(x)\right ) y'(x)-1=0 \]

✓ Mathematica : cpu = 0.115956 (sec), leaf count = 76

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

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

✓ Maple : cpu = 0.142 (sec), leaf count = 78

dsolve((x^2*y(x)^3+x*y(x))*diff(y(x),x)-1 = 0,y(x))
 

\[y \left (x \right ) = \frac {\sqrt {2 x^{2} \operatorname {LambertW}\left (\frac {c_{1} {\mathrm e}^{-\frac {2 x -1}{2 x}}}{2}\right )+2 x^{2}-x}}{x}\]