70.1.12 problem 2.2 (vi)

Internal problem ID [14302]
Book : Nonlinear Ordinary Differential Equations by D.W.Jordna and P.Smith. 4th edition 1999. Oxford Univ. Press. NY
Section : Chapter 2. Plane autonomous systems and linearization. Problems page 79
Problem number : 2.2 (vi)
Date solved : Tuesday, January 28, 2025 at 06:26:00 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 15

dsolve([diff(x(t),t)=x(t),diff(y(t),t)=y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 57

DSolve[{D[x[t],t]==x[t],D[y[t],t]==y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 e^t \\ y(t)\to c_2 e^t \\ x(t)\to c_1 e^t \\ y(t)\to 0 \\ x(t)\to 0 \\ y(t)\to c_2 e^t \\ x(t)\to 0 \\ y(t)\to 0 \\ \end{align*}