74.6.8 problem 9

Internal problem ID [16031]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 08:28:16 AM
CAS classification : [[_homogeneous, `class G`], _exact]

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

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.191 (sec). Leaf size: 19

DSolve[Log[t*y[t]]+t/y[t]*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{1+\frac {c_1}{t}}}{t} \]