2.1411   ODE No. 1411

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

✓ Mathematica : cpu = 0.248322 (sec), leaf count = 42

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

\[\left \{\left \{y(x)\to c_1 \left (e^{-x}+1\right )+c_2 e^{-x} \left (e^x \log \left (e^x+1\right )+\log \left (e^x+1\right )+1\right )\right \}\right \}\]

✓ Maple : cpu = 0.039 (sec), leaf count = 27

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

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