ODE No. 839

\[ y'(x)=\frac {e^{\frac {y(x)}{x}} \left (x^2+x e^{-\frac {y(x)}{x}}+e^{-\frac {y(x)}{x}} y(x)\right )}{x} \] Mathematica : cpu = 0.281035 (sec), leaf count = 28

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

\[\left \{\left \{y(x)\to -x \log \left (-\frac {x}{2}+\frac {e^{2 c_1}}{2 x}\right )\right \}\right \}\] Maple : cpu = 0.072 (sec), leaf count = 19

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

\[y \left (x \right ) = \ln \left (\frac {2 x}{-x^{2}+c_{1}}\right ) x\]