Internal problem ID [11557]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 218
Problem number: 2(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-x+y \left (t \right )\\ y^{\prime }\left (t \right )&=-3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 28
dsolve([diff(x(t),t)=-x(t)+y(t),diff(y(t),t)=-3*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {c_{2} {\mathrm e}^{-3 t}}{2}+{\mathrm e}^{-t} c_{1} \] \[ y \left (t \right ) = c_{2} {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 43
DSolve[{x'[t]==-x[t]+y[t],y'[t]==-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-3 t} \left ((2 c_1+c_2) e^{2 t}-c_2\right ) y(t)\to c_2 e^{-3 t} \end{align*}