65.3.9 problem 8.5

Internal problem ID [13727]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 8, Separable equations. Exercises page 72
Problem number : 8.5
Date solved : Tuesday, January 28, 2025 at 05:59:53 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

\[ x \left (t \right ) = c_{1} {\mathrm e}^{\lambda t} \]

✓ 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*}