63.4.2 problem 1(b)

Internal problem ID [13045]
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)
Date solved : Tuesday, January 28, 2025 at 04:50:04 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&={\mathrm e}^{-2 x} \end{align*}

With initial conditions

\begin{align*} x \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.058 (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: 0.004 (sec). Leaf size: 17

DSolve[{D[x[t],t]==Exp[-2*x[t]],{x[0]==1}},x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{2} \log \left (2 t+e^2\right ) \]