38.6.1 problem 1

Internal problem ID [8431]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 05:36:39 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=5 y \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 10

ode:=diff(y(x),x) = 5*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{5 x} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

ode=D[y[x],x]==5*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{5 x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.059 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{5 x} \]