Internal problem ID [11435]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
\[ \boxed {x^{\prime }-x \left (1+x \,{\mathrm e}^{t}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(x(t),t)=x(t)*(1+x(t)*exp(t)),x(t), singsol=all)
\[ x \left (t \right ) = \frac {2}{2 \,{\mathrm e}^{-t} c_{1} -{\mathrm e}^{t}} \]
✓ Solution by Mathematica
Time used: 0.323 (sec). Leaf size: 27
DSolve[x'[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*}