63.4.20 problem 10(a)

Internal problem ID [13063]
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 : 10(a)
Date solved : Tuesday, January 28, 2025 at 04:50:54 AM
CAS classification : [_separable]

\begin{align*} x^{\prime }&={\mathrm e}^{t +x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 13

dsolve([diff(x(t),t)=exp(t+x(t)),x(0) = 0],x(t), singsol=all)
 

\[ x \left (t \right ) = -\ln \left (2-{\mathrm e}^{t}\right ) \]

✓ Solution by Mathematica

Time used: 0.763 (sec). Leaf size: 15

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

\[ x(t)\to -\log \left (2-e^t\right ) \]