Internal problem ID [7315]
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]]
\[ \boxed {y^{\prime \prime }+{\mathrm e}^{y}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+exp(y(x))=0,y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (-\frac {\tanh \left (\frac {x +c_{2}}{2 c_{1}}\right )^{2}-1}{2 c_{1}^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 29.642 (sec). Leaf size: 60
DSolve[y''[x]+Exp[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \log \left (\frac {1}{2} c_1 \text {sech}^2\left (\frac {1}{2} \sqrt {c_1 (x+c_2){}^2}\right )\right ) y(x)\to \log \left (\frac {1}{2} c_1 \text {sech}^2\left (\frac {\sqrt {c_1 x^2}}{2}\right )\right ) \end{align*}