2.565   ODE No. 565

\[ y'(x)+y(x) \log \left (y'(x)\right )-x y(x)-y(x) \log (y(x))=0 \]

✓ Mathematica : cpu = 0.0358012 (sec), leaf count = 25

DSolve[-(x*y[x]) - Log[y[x]]*y[x] + Log[Derivative[1][y][x]]*y[x] + Derivative[1][y][x] == 0,y[x],x]
 

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

✓ Maple : cpu = 0.35 (sec), leaf count = 17

dsolve(y(x)*ln(diff(y(x),x))+diff(y(x),x)-y(x)*ln(y(x))-x*y(x)=0,y(x))
 

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