Internal problem ID [10514]
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 }\left (t \right )&=-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-4 x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 52
dsolve([diff(x(t),t)=-2*y(t),diff(y(t),t)=-4*x(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {\sqrt {2}\, \left (c_{1} {\mathrm e}^{2 \sqrt {2}\, t}-c_{2} {\mathrm e}^{-2 \sqrt {2}\, t}\right )}{2} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{2 \sqrt {2}\, t}+c_{2} {\mathrm e}^{-2 \sqrt {2}\, t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 70
DSolve[{x'[t]==-2*y[t],y'[t]==-4*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cosh \left (2 \sqrt {2} t\right )-\frac {c_2 \sinh \left (2 \sqrt {2} t\right )}{\sqrt {2}} \\ y(t)\to c_2 \cosh \left (2 \sqrt {2} t\right )-\sqrt {2} c_1 \sinh \left (2 \sqrt {2} t\right ) \\ \end{align*}