73.27.10 problem 38.10 (d)

Internal problem ID [15766]
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)
Date solved : Tuesday, January 28, 2025 at 08:06:50 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=8 x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 35

dsolve([diff(x(t),t)=-2*y(t),diff(y(t),t)=8*x(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} \sin \left (4 t \right )+c_{2} \cos \left (4 t \right ) \\ y \left (t \right ) &= -2 \cos \left (4 t \right ) c_{1} +2 \sin \left (4 t \right ) c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 42

DSolve[{D[x[t],t]==-2*y[t],D[y[t],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*}