81.1.6 problem 2-4

Internal problem ID [21451]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 2. Separable differential equations
Problem number : 2-4
Date solved : Thursday, October 02, 2025 at 07:38:22 PM
CAS classification : [_quadrature]

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

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

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: 0.016 (sec). Leaf size: 18

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: 0.056 (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)
 

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