79.2.1 problem 1

Internal problem ID [18514]
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 : Tuesday, January 28, 2025 at 11:51:38 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[x[t],t]==\[Lambda]*x[t],x[t],t,IncludeSingularSolutions -> True]
 

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