79.1.8 problem 2 (ii)

Internal problem ID [18495]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 2 (ii)
Date solved : Tuesday, January 28, 2025 at 11:50:56 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=b \,{\mathrm e}^{x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 14

dsolve([diff(x(t),t)=b*exp(x(t)),x(0) = 1],x(t), singsol=all)
 

\[ x = -\ln \left (-b t +{\mathrm e}^{-1}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 17

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

\[ x(t)\to 1-\log (1-e b t) \]