65.13.1 problem 1

Internal problem ID [15808]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:28:13 AM
CAS classification : [_quadrature]

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

Using Laplace method

✓ Maple. Time used: 0.078 (sec). Leaf size: 9

ode:=diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x),method='laplace');
 

\[ y = y \left (0\right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.016 (sec). Leaf size: 7

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

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