Internal problem ID [12784]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.4 page 310
Problem number: 9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 y\\ y^{\prime }&=-2 x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(x(t),t) = 2*y(t), diff(y(t),t) = -2*x(t), x(0) = 1, y(0) = 0],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = \cos \left (2 t \right ) y \left (t \right ) = -\sin \left (2 t \right ) \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 18
DSolve[{x'[t]==0*x[t]+2*y[t],y'[t]==-2*x[t]+0*y[t]},{x[0]==1,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \cos (2 t) y(t)\to -\sin (2 t) \end{align*}