Internal problem ID [4483]
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: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\frac {t y^{\prime }}{y}+1+\ln \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve((t/y(t))*diff(y(t),t)+(1+ln(y(t)))=0,y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-\frac {t c_{1}-1}{t c_{1}}} \]
✓ Solution by Mathematica
Time used: 0.365 (sec). Leaf size: 24
DSolve[(t/y[t])*y'[t]+(1+Log[y[t]])==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-1+\frac {e^{c_1}}{t}} \\ y(t)\to \frac {1}{e} \\ \end{align*}