36.3.13 problem 14

Internal problem ID [6334]
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
Date solved : Monday, January 27, 2025 at 01:56:51 PM
CAS classification : [_separable]

\begin{align*} \frac {t y^{\prime }}{y}+1+\ln \left (y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 18

dsolve((t/y(t))*diff(y(t),t)+(1+ln(y(t)))=0,y(t), singsol=all)
 

\[ y = {\mathrm e}^{\frac {-t c_1 +1}{c_1 t}} \]

✓ Solution by Mathematica

Time used: 0.262 (sec). Leaf size: 24

DSolve[(t/y[t])*D[y[t],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*}