68.4.67 problem 64

Internal problem ID [17247]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 64
Date solved : Thursday, October 02, 2025 at 01:59:53 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=-y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(y(t),t) = -y(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 18

ode=D[y[t],t]==-y[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_1 e^{-t}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.054 (sec). Leaf size: 7

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

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