36.1.9 problem 9

Internal problem ID [6264]
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
Date solved : Monday, January 27, 2025 at 01:50:30 PM
CAS classification : [_separable]

\begin{align*} x^{\prime }&=\frac {t \,{\mathrm e}^{-t -2 x}}{x} \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 25

dsolve(diff(x(t),t)=t/(x(t)*exp(t+2*x(t))),x(t), singsol=all)
 

\[ x \left (t \right ) = \frac {\operatorname {LambertW}\left (-4 \left (-c_{1} {\mathrm e}^{t}+t +1\right ) {\mathrm e}^{-t -1}\right )}{2}+\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 60.188 (sec). Leaf size: 31

DSolve[D[x[t],t]==t/(x[t]*Exp[t+2*x[t]]),x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{2} \left (1+W\left (-4 e^{-t-1} \left (t-c_1 e^t+1\right )\right )\right ) \]