Internal problem ID [11542]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 202
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-2 x-y \left (t \right )\\ y^{\prime }\left (t \right )&=-4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve([diff(x(t),t)=-2*x(t)-y(t),diff(y(t),t)=-4*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {c_{2} {\mathrm e}^{-4 t}}{2}+c_{1} {\mathrm e}^{-2 t} \\ y \left (t \right ) &= c_{2} {\mathrm e}^{-4 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 43
DSolve[{x'[t]==-2*x[t]-y[t],y'[t]==-4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-4 t} \left ((2 c_1-c_2) e^{2 t}+c_2\right ) \\ y(t)\to c_2 e^{-4 t} \\ \end{align*}