ODE No. 830

\[ y'(x)=\frac {(x-y(x)) y(x)}{x \left (-y(x)^4-y(x)^3-y(x)+x\right )} \] Mathematica : cpu = 0.427055 (sec), leaf count = 37

DSolve[Derivative[1][y][x] == ((x - y[x])*y[x])/(x*(x - y[x] - y[x]^3 - y[x]^4)),y[x],x]
 

\[\text {Solve}\left [-\frac {1}{3} y(x)^3-\frac {y(x)^2}{2}-\frac {x}{y(x)}-\log (y(x))+\log (x)=c_1,y(x)\right ]\] Maple : cpu = 0.197 (sec), leaf count = 38

dsolve(diff(y(x),x) = y(x)*(x-y(x))/x/(x-y(x)-y(x)^3-y(x)^4),y(x))
 

\[y \left (x \right ) = {\mathrm e}^{\RootOf \left (2 \,{\mathrm e}^{4 \textit {\_Z}}+3 \,{\mathrm e}^{3 \textit {\_Z}}-6 \ln \left (x \right ) {\mathrm e}^{\textit {\_Z}}+6 \,{\mathrm e}^{\textit {\_Z}} c_{1}+6 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+6 x \right )}\]