57.4.20 problem 10(a)

Internal problem ID [14344]
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 : Thursday, October 02, 2025 at 09:31:59 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*}

✓ Maple. Time used: 0.065 (sec). Leaf size: 13

ode:=diff(x(t),t) = exp(t+x(t)); 
ic:=[x(0) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.576 (sec). Leaf size: 15

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

\begin{align*} x(t)&\to -\log \left (2-e^t\right ) \end{align*}

✓ Sympy. Time used: 0.117 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-exp(t + x(t)) + Derivative(x(t), t),0) 
ics = {x(0): 0} 
dsolve(ode,func=x(t),ics=ics)
 

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