2.633   ODE No. 633

\[ y'(x)=\frac {e^{2 x/3}}{e^{-2 x/3} y(x)+1} \]

✓ Mathematica : cpu = 0.175241 (sec), leaf count = 85

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

\[\text {Solve}\left [7 \left (3 \log \left (-\frac {2}{3} e^{-4 x/3} y(x)^2-\frac {2}{3} e^{-2 x/3} y(x)+1\right )+4 x-9 c_1\right )=6 \sqrt {7} \tanh ^{-1}\left (\frac {y(x)+4 e^{2 x/3}}{\sqrt {7} \left (y(x)+e^{2 x/3}\right )}\right ),y(x)\right ]\]

✓ Maple : cpu = 1.253 (sec), leaf count = 52

dsolve(diff(y(x),x) = 1/(y(x)*exp(-2/3*x)+1)*exp(2/3*x),y(x))
 

\[y \left (x \right ) = \operatorname {RootOf}\left (-{\mathrm e}^{\operatorname {RootOf}\left (343-343 \tanh \left (\frac {\left (4 c_{1} -4 x -3 \textit {\_Z} \right ) \sqrt {7}}{6}\right )^{2}+98 \,{\mathrm e}^{\textit {\_Z}}\right )}-3+2 \textit {\_Z} +2 \textit {\_Z}^{2}\right ) {\mathrm e}^{\frac {2 x}{3}}\]