43.1.11 problem 5(a)

Internal problem ID [8876]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.3 Introduction– Linear equations of First Order. Page 38
Problem number : 5(a)
Date solved : Tuesday, September 30, 2025 at 05:58:14 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: 0.015 (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: 0.056 (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)
 

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