Internal problem ID [12101]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 28, Distinct real eigenvalues. Exercises page 282
Problem number: 28.6 (iii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve([diff(x(t),t)=-2*x(t)+2*y(t),diff(y(t),t)=x(t)-y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{-3 t} \\ y \left (t \right ) &= -\frac {c_{2} {\mathrm e}^{-3 t}}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 71
DSolve[{x'[t]==-2*x[t]+2*y[t],y'[t]==x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-3 t} \left (c_1 \left (e^{3 t}+2\right )+2 c_2 \left (e^{3 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-3 t} \left (c_1 \left (e^{3 t}-1\right )+c_2 \left (2 e^{3 t}+1\right )\right ) \\ \end{align*}