7.14 problem 1604 (6.14)

Internal problem ID [9179]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 6, non-linear second order
Problem number: 1604 (6.14).
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: 0.375 (sec). Leaf size: 23

dsolve(diff(diff(y(x),x),x)-exp(y(x))=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \ln \left (\frac {\tan \left (\frac {x +c_{2}}{2 c_{1}}\right )^{2}+1}{2 c_{1}^{2}}\right ) \]

Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 26

DSolve[-E^y[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \log \left (-\frac {c_1}{1+\cosh \left (\sqrt {c_1} (x+c_2)\right )}\right ) \\ \end{align*}