Internal problem ID [13710]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 38. Systems of differential equations. A starting point. Additional Exercises.
page 786
Problem number: 38.10 (d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=8 x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve([diff(x(t),t)=-2*y(t),diff(y(t),t)=8*x(t)],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {c_{1} \cos \left (4 t \right )}{2}-\frac {c_{2} \sin \left (4 t \right )}{2} y \left (t \right ) = c_{1} \sin \left (4 t \right )+c_{2} \cos \left (4 t \right ) \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 42
DSolve[{x'[t]==-2*y[t],y'[t]==8*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (4 t)-\frac {1}{2} c_2 \sin (4 t) y(t)\to c_2 \cos (4 t)+2 c_1 \sin (4 t) \end{align*}