ODE
\[ a e^{y(x)}+y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.212842 (sec), leaf count = 35
\[\left \{\left \{y(x)\to \log \left (\frac {c_1 \text {sech}^2\left (\frac {1}{2} \sqrt {c_1 (x+c_2){}^2}\right )}{2 a}\right )\right \}\right \}\]
Maple ✓
cpu = 0.697 (sec), leaf count = 26
\[\left [y \left (x \right ) = \ln \left (-\frac {\tanh ^{2}\left (\frac {x +\textit {\_C2}}{2 \textit {\_C1}}\right )-1}{2 a \,\textit {\_C1}^{2}}\right )\right ]\] Mathematica raw input
DSolve[a*E^y[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Log[(C[1]*Sech[Sqrt[C[1]*(x + C[2])^2]/2]^2)/(2*a)]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+a*exp(y(x)) = 0, y(x))
Maple raw output
[y(x) = ln(-1/2*(tanh(1/2*(x+_C2)/_C1)^2-1)/a/_C1^2)]