Internal problem ID [11532]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 190
Problem number: 2(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-4 x \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 52
dsolve([diff(x(t),t)=-2*y(t),diff(y(t),t)=-4*x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{2 \sqrt {2}\, t}+c_{2} {\mathrm e}^{-2 \sqrt {2}\, t} \\ y \left (t \right ) &= -\sqrt {2}\, \left (c_{1} {\mathrm e}^{2 \sqrt {2}\, t}-c_{2} {\mathrm e}^{-2 \sqrt {2}\, t}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 111
DSolve[{x'[t]==-2*y[t],y'[t]==-4*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} e^{-2 \sqrt {2} t} \left (2 c_1 \left (e^{4 \sqrt {2} t}+1\right )-\sqrt {2} c_2 \left (e^{4 \sqrt {2} t}-1\right )\right ) \\ y(t)\to \frac {1}{2} e^{-2 \sqrt {2} t} \left (c_2 \left (e^{4 \sqrt {2} t}+1\right )-\sqrt {2} c_1 \left (e^{4 \sqrt {2} t}-1\right )\right ) \\ \end{align*}