68.6.9 problem 10

Internal problem ID [17319]
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 : Thursday, October 02, 2025 at 02:02:28 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 9

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

\[ y = \frac {c_1}{t} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 11

ode=Exp[t*y[t]]+t*Exp[t*y[t]]/y[t]*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {c_1}{t} \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 5

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*exp(t*y(t))*Derivative(y(t), t)/y(t) + exp(t*y(t)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1}}{t} \]