Internal problem ID [11791]
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: 0.0 (sec). Leaf size: 21
dsolve([diff(x(t),t)=-x(t)+y(t),diff(y(t),t)=-x(t)+y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = c_{1} t -c_{1} +c_{2} \] \[ y \left (t \right ) = c_{1} t +c_{2} \]
✓ 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*}