Internal problem ID [13197]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.7 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y^{\prime \prime }+y^{\prime } {\mathrm e}^{-y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 11
dsolve([diff(y(x),x$2)=-diff(y(x),x)*exp(-y(x)),y(0) = 0, D(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (2 \,{\mathrm e}^{x}-1\right ) \]
✓ Solution by Mathematica
Time used: 5.75 (sec). Leaf size: 13
DSolve[{y''[x]==-y'[x]*Exp[-y[x]],{y[0]==0,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \log \left (2 e^x-1\right ) \]