ODE No. 763

\[ y'(x)=\frac {y(x) (x \log (y(x))+\log (y(x))+x)}{x (x+1)} \]

✓ Mathematica : cpu = 0.120406 (sec), leaf count = 22

DSolve[Derivative[1][y][x] == ((x + Log[y[x]] + x*Log[y[x]])*y[x])/(x*(1 + x)),y[x],x]

\[\left \{\left \{y(x)\to x^x (x+1)^{-x} e^{c_1 x}\right \}\right \}\]

✓ Maple : cpu = 0.085 (sec), leaf count = 14

dsolve(diff(y(x),x) = (ln(y(x))*x+ln(y(x))+x)*y(x)/x/(1+x),y(x))

\[y \left (x \right ) = \left (\frac {c_{1} x}{1+x}\right )^{x}\]