90.1.24 problem 35

Internal problem ID [25048]
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 : 35
Date solved : Thursday, October 02, 2025 at 11:47:50 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=-9 \\ \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 11

ode:=(t+1)*diff(y(t),t)+y(t) = 0; 
ic:=[y(1) = -9]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\frac {18}{t +1} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 12

ode=(t+1)*D[y[t],{t,1}]+y[t]==0; 
ic={y[1]==-9}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {18}{t+1} \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((t + 1)*Derivative(y(t), t) + y(t),0) 
ics = {y(1): -9} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {18}{t + 1} \]