7.24.1 problem 11

Internal problem ID [601]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.3 (Matrices and linear systems). Problems at page 364
Problem number : 11
Date solved : Wednesday, February 05, 2025 at 03:45:59 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-3 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 34

dsolve([diff(x(t),t)=-3*y(t),diff(y(t),t)=3*x(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= \sin \left (3 t \right ) c_1 +\cos \left (3 t \right ) c_2 \\ y \left (t \right ) &= -\cos \left (3 t \right ) c_1 +\sin \left (3 t \right ) c_2 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 39

DSolve[{D[x[t],t]==-3*y[t],D[y[t],t]==3*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 \cos (3 t)-c_2 \sin (3 t) \\ y(t)\to c_2 \cos (3 t)+c_1 \sin (3 t) \\ \end{align*}