Internal problem ID [4482]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page
64
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {{\mathrm e}^{t} \left (y-t \right )+\left (1+{\mathrm e}^{t}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(exp(t)*(y(t)-t)+(1+exp(t))*diff(y(t),t)=0,y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (t -1\right ) {\mathrm e}^{t}+c_{1}}{1+{\mathrm e}^{t}} \]
✓ Solution by Mathematica
Time used: 0.122 (sec). Leaf size: 23
DSolve[Exp[t]*(y[t]-t)+(1+Exp[t])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^t (t-1)+c_1}{e^t+1} \\ \end{align*}