ODE No. 870

\[ y'(x)=\frac {e^{\frac {y(x)}{x}} \left (x^4+x^3+x e^{-\frac {y(x)}{x}}+e^{-\frac {y(x)}{x}} y(x)+x\right )}{x} \]

✓ Mathematica : cpu = 0.788632 (sec), leaf count = 35

DSolve[Derivative[1][y][x] == (E^(y[x]/x)*(x + x/E^(y[x]/x) + x^3 + x^4 + y[x]/E^(y[x]/x)))/x,y[x],x]

\[\left \{\left \{y(x)\to -x \log \left (\frac {-\frac {x^4}{4}-\frac {x^3}{3}-x-c_1}{x}\right )\right \}\right \}\]

✓ Maple : cpu = 0.851 (sec), leaf count = 30

dsolve(diff(y(x),x) = (exp(-y(x)/x)*y(x)+exp(-y(x)/x)*x+x+x^3+x^4)*exp(y(x)/x)/x,y(x))

\[y \left (x \right ) = -\ln \left (-\frac {3 x^{4}+4 x^{3}+12 c_{1} +12 x}{12 x}\right ) x\]