63.22.8 problem 4(h)

Internal problem ID [13238]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 4, Linear Systems. Exercises page 237
Problem number : 4(h)
Date solved : Tuesday, January 28, 2025 at 05:12:51 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=9 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 35

dsolve([diff(x(t),t)=0*x(t)+9*y(t),diff(y(t),t)=-x(t)+0*y(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right ) \\ y &= \frac {\cos \left (3 t \right ) c_{1}}{3}-\frac {\sin \left (3 t \right ) c_{2}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 42

DSolve[{D[x[t],t]==0*x[t]+9*y[t],D[y[t],t]==-x[t]+0*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to c_1 \cos (3 t)+3 c_2 \sin (3 t) \\ y(t)\to c_2 \cos (3 t)-\frac {1}{3} c_1 \sin (3 t) \\ \end{align*}