Internal problem ID [10544]
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).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=9 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 36
dsolve([diff(x(t),t)=0*x(t)+9*y(t),diff(y(t),t)=-x(t)+0*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -3 c_{1} \cos \left (3 t \right )+3 c_{2} \sin \left (3 t \right ) \] \[ y \left (t \right ) = c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 42
DSolve[{x'[t]==0*x[t]+9*y[t],y'[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*}