\[ y''(x)-e^{y(x)}=0 \] ✓ Mathematica : cpu = 0.0404187 (sec), leaf count = 34
DSolve[-E^y[x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \log \left (\frac {1}{2} c_1 \left (-1+\tanh ^2\left (\frac {1}{2} \sqrt {c_1 (x+c_2){}^2}\right )\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.231 (sec), leaf count = 23
dsolve(diff(diff(y(x),x),x)-exp(y(x))=0,y(x))
\[y \left (x \right ) = \ln \left (\frac {\tan ^{2}\left (\frac {x +c_{2}}{2 c_{1}}\right )+1}{2 c_{1}^{2}}\right )\]