63.5.27 problem 15(b)

Internal problem ID [13101]
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 1.4.1. Integrating factors. Exercises page 41
Problem number : 15(b)
Date solved : Tuesday, January 28, 2025 at 04:52:22 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Bernoulli]

\begin{align*} x^{\prime }&=x \left (1+x \,{\mathrm e}^{t}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(diff(x(t),t)=x(t)*(1+x(t)*exp(t)),x(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 27

DSolve[D[x[t],t]==x[t]*(1+x[t]*Exp[t]),x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -\frac {2 e^t}{e^{2 t}-2 c_1} \\ x(t)\to 0 \\ \end{align*}