12.2.1 problem 1

Internal problem ID [1537]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 1
Date solved : Tuesday, March 04, 2025 at 12:38:30 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.104 (sec). Leaf size: 8

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

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