ODE No. 702

\[ y'(x)=\frac {-x^3+x^3 (-\log (x))-x y(x)^2+x y(x)-e^x y(x)-x y(x)^2 \log (x)}{x \left (x-e^x\right )} \] Mathematica : cpu = 2.40073 (sec), leaf count = 37

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

\[\left \{\left \{y(x)\to x \tan \left (\int _1^x\frac {K[1] (\log (K[1])+1)}{e^{K[1]}-K[1]}dK[1]+c_1\right )\right \}\right \}\] Maple : cpu = 0.095 (sec), leaf count = 35

dsolve(diff(y(x),x) = (-y(x)*exp(x)+x*y(x)-x^3*ln(x)-x^3-x*y(x)^2*ln(x)-x*y(x)^2)/(-exp(x)+x)/x,y(x))
 

\[y \left (x \right ) = \tan \left (\int \frac {x \ln \left (x \right )}{{\mathrm e}^{x}-x}d x +\int \frac {x}{{\mathrm e}^{x}-x}d x +c_{1}\right ) x\]