Internal problem ID [4412]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{\prime }-\frac {t \,{\mathrm e}^{-t -2 x}}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 26
dsolve(diff(x(t),t)=t/(x(t)*exp(t+2*x(t))),x(t), singsol=all)
\[ x \relax (t ) = \frac {\LambertW \left (\left (4 c_{1} {\mathrm e}^{t}-4 t -4\right ) {\mathrm e}^{-t -1}\right )}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 60.275 (sec). Leaf size: 31
DSolve[x'[t]==t/(x[t]*Exp[t+2*x[t]]),x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} \left (1+\text {ProductLog}\left (-4 e^{-t-1} \left (t-c_1 e^t+1\right )\right )\right ) \\ \end{align*}