2.317   ODE No. 317

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

✓ Mathematica : cpu = 0.222714 (sec), leaf count = 23

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

\[\text {Solve}\left [y(x)^2-\frac {x}{y(x)}+\log (y(x))+\log (x)=c_1,y(x)\right ]\]

✓ Maple : cpu = 0.154 (sec), leaf count = 29

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

\[y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-{\mathrm e}^{3 \textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (x \right )+{\mathrm e}^{\textit {\_Z}} c_{1} -\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \right )}\]