70.1.8 problem 2.2 (ii)

Internal problem ID [14298]
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 (ii)
Date solved : Tuesday, January 28, 2025 at 06:25:57 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=x \left (t \right )-y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=2 x \left (t \right )-2 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 24

dsolve([diff(x(t),t)=x(t)-y(t),diff(y(t),t)=2*x(t)-2*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 59

DSolve[{D[x[t],t]==x[t]-y[t],D[y[t],t]==2*x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{-t} \left (c_1 \left (2 e^t-1\right )-c_2 \left (e^t-1\right )\right ) \\ y(t)\to e^{-t} \left (2 c_1 \left (e^t-1\right )-c_2 \left (e^t-2\right )\right ) \\ \end{align*}