Internal problem ID [11397]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-{\mathrm e}^{t +x}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 13
dsolve([diff(x(t),t)=exp(t+x(t)),x(0) = 0],x(t), singsol=all)
\[ x \left (t \right ) = -\ln \left (-{\mathrm e}^{t}+2\right ) \]
✓ Solution by Mathematica
Time used: 1.309 (sec). Leaf size: 15
DSolve[{x'[t]==Exp[t+x[t]],{x[0]==0}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -\log \left (2-e^t\right ) \]