74.6.8 problem 9

Internal problem ID [15960]
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 : Monday, March 31, 2025 at 02:16:40 PM
CAS classification : [[_homogeneous, `class G`], _exact]

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

✓ Maple. Time used: 0.114 (sec). Leaf size: 16

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

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

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

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

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

✓ Sympy. Time used: 0.507 (sec). Leaf size: 10

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

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