44.1.4 problem 1(d)

Internal problem ID [9062]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 1(d)
Date solved : Tuesday, September 30, 2025 at 06:03:21 PM
CAS classification : [_quadrature]

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

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

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 18

ode=D[y[x],x]==k*y[x]; 
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: 0.059 (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)
 

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