ODE No. 840

\[ y'(x)=\frac {e^{\frac {y(x)}{x}} \left (x^3+x e^{-\frac {y(x)}{x}}+e^{-\frac {y(x)}{x}} y(x)\right )}{x} \] Mathematica : cpu = 0.289763 (sec), leaf count = 30

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

\[\left \{\left \{y(x)\to -x \log \left (-\frac {x^2}{3}+\frac {e^{3 c_1}}{3 x}\right )\right \}\right \}\] Maple : cpu = 0.07 (sec), leaf count = 19

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

\[y \left (x \right ) = \ln \left (\frac {3 x}{-x^{3}+c_{1}}\right ) x\]