Internal problem ID [12242]
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).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )-2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(x(t),t)=x(t)-y(t),diff(y(t),t)=2*x(t)-2*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {c_{2} {\mathrm e}^{-t}}{2}+c_{1} \] \[ y \left (t \right ) = c_{1} +c_{2} {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 59
DSolve[{x'[t]==x[t]-y[t],y'[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*}