Internal problem ID [13061]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.1. page 258
Problem number: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-y\\ y^{\prime }&=x \left (t \right )-y \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
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+1)-c_2 t \\ y(t)\to (c_1-c_2) t+c_2 \\ \end{align*}