Internal problem ID [12111]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 30, A repeated real eigenvalue. Exercises page 299
Problem number: 30.5 (iii).
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 )&=-x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve([diff(x(t),t)=-x(t)+y(t),diff(y(t),t)=-x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} t +c_{2} \\ y \left (t \right ) &= c_{1} t +c_{1} +c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 32
DSolve[{x'[t]==-x[t]+y[t],y'[t]==-x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 (-t)+c_2 t+c_1 \\ y(t)\to (c_2-c_1) t+c_2 \\ \end{align*}