2.211   ODE No. 211

\[ y(x) y'(x)-x e^{\frac {x}{y(x)}}=0 \]

✓ Mathematica : cpu = 0.213568 (sec), leaf count = 41

DSolve[-(E^(x/y[x])*x) + y[x]*Derivative[1][y][x] == 0,y[x],x]
 

\[\text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]}{K[1]^2-e^{\frac {1}{K[1]}}}dK[1]=-\log (x)+c_1,y(x)\right ]\]

✓ Maple : cpu = 0.053 (sec), leaf count = 31

dsolve(y(x)*diff(y(x),x)-x*exp(x/y(x)) = 0,y(x))
 

\[y \left (x \right ) = \operatorname {RootOf}\left (-\left (\int _{}^{\textit {\_Z}}\frac {\textit {\_a}}{-\textit {\_a}^{2}+{\mathrm e}^{\frac {1}{\textit {\_a}}}}d \textit {\_a} \right )+\ln \left (x \right )+c_{1} \right ) x\]