Internal problem ID [6562]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+{\mathrm e}^{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.061 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+exp(y(x))=0,y(x), singsol=all)
\[ y \relax (x ) = \ln \left (-\frac {\tanh ^{2}\left (\frac {c_{2}+x}{2 c_{1}}\right )-1}{2 c_{1}^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 0.978 (sec). Leaf size: 31
DSolve[y''[x]+Exp[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\log (2)+\log \left (c_1 \text {sech}^2\left (\frac {1}{2} \sqrt {c_1} (x+c_2)\right )\right ) \\ \end{align*}