2.823   ODE No. 823

\[ y'(x)=\frac {y(x) (y(x)+x)}{x \left (y(x)^4+y(x)^3+y(x)+x\right )} \]

✓ Mathematica : cpu = 0.26006 (sec), leaf count = 39

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

\[\text {Solve}\left [\frac {y(x)^3}{3}+\frac {y(x)^2}{2}+\log (y(x))-\frac {y(x) \log (x)+x}{y(x)}=c_1,y(x)\right ]\]

✓ Maple : cpu = 0.112 (sec), leaf count = 38

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

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