74.6.9 problem 10

Internal problem ID [16032]
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 : 10
Date solved : Tuesday, January 28, 2025 at 08:28:18 AM
CAS classification : [_separable]

\begin{align*} {\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 9

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

\[ y = \frac {c_{1}}{t} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 11

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

\[ y(t)\to \frac {c_1}{t} \]