79.2.1 problem 1

Internal problem ID [18435]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 4. Autonomous systems. Exercises at page 69
Problem number : 1
Date solved : Thursday, March 13, 2025 at 11:57:04 AM
CAS classification : [_quadrature]

\begin{align*} x^{\prime }&=-\lambda x \end{align*}

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

ode:=diff(x(t),t) = -lambda*x(t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_{1} {\mathrm e}^{-\lambda t} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 18

ode=D[x[t],t]==\[Lambda]*x[t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)\to c_1 e^{\lambda t} \\ x(t)\to 0 \\ \end{align*}

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

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

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