68.4.13 problem 13

Internal problem ID [17193]
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 : 13
Date solved : Thursday, October 02, 2025 at 01:50:05 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+k y&=0 \end{align*}

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

ode:=diff(y(x),x)+k*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 19

ode=D[y[x],x]+k*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.060 (sec). Leaf size: 8

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

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