Internal problem ID [11541]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 190
Problem number: 2(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 48
dsolve([diff(x(t),t)=-3*y(t),diff(y(t),t)=2*x(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {\sqrt {6}\, \left (\cos \left (\sqrt {6}\, t \right ) c_{1} -\sin \left (\sqrt {6}\, t \right ) c_{2} \right )}{2} \] \[ y \left (t \right ) = c_{1} \sin \left (\sqrt {6}\, t \right )+c_{2} \cos \left (\sqrt {6}\, t \right ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 69
DSolve[{x'[t]==-3*y[t],y'[t]==2*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos \left (\sqrt {6} t\right )-\sqrt {\frac {3}{2}} c_2 \sin \left (\sqrt {6} t\right ) y(t)\to c_2 \cos \left (\sqrt {6} t\right )+\sqrt {\frac {2}{3}} c_1 \sin \left (\sqrt {6} t\right ) \end{align*}