Internal problem ID [12561]
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 (i).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve([diff(x(t),t)=3*x(t)-y(t),diff(y(t),t)=x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 44
DSolve[{x'[t]==3*x[t]-y[t],y'[t]==x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{2 t} (c_1 (t+1)-c_2 t) \\ y(t)\to e^{2 t} ((c_1-c_2) t+c_2) \\ \end{align*}