Internal problem ID [10535]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 4, Linear Systems. Exercises page 225
Problem number: 1(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=-3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 24
dsolve([diff(x(t),t)=-3*x(t)+y(t),diff(y(t),t)=-3*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \left (t c_{2} +c_{1} \right ) {\mathrm e}^{-3 t} \] \[ y \left (t \right ) = c_{2} {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 29
DSolve[{x'[t]==-3*x[t]+y[t],y'[t]==-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-3 t} (c_2 t+c_1) \\ y(t)\to c_2 e^{-3 t} \\ \end{align*}