23.1.9 problem 1(i)

Internal problem ID [4099]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 1(i)
Date solved : Sunday, March 30, 2025 at 02:17:54 AM
CAS classification : [_quadrature]

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

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

ode:=diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 18

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: 0.097 (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)
 

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