90.1.13 problem 24

Internal problem ID [25037]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 13
Problem number : 24
Date solved : Thursday, October 02, 2025 at 11:47:42 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

ode:=(t+1)*diff(y(t),t)+y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {c_1}{t +1} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

ode=(t+1)*D[y[t],{t,1}]+y[t]== 0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {c_1}{t+1}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.125 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t + 1)*Derivative(y(t), t) + y(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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