Internal problem ID [11379]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises
page 26
Problem number: 1(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x^{\prime }-{\mathrm e}^{-2 x}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 13
dsolve([diff(x(t),t)=exp(-2*x(t)),x(0) = 1],x(t), singsol=all)
\[ x \left (t \right ) = \frac {\ln \left (2 t +{\mathrm e}^{2}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 17
DSolve[{x'[t]==Exp[-2*x[t]],{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{2} \log \left (2 t+e^2\right ) \]