7.22.3 problem 13

Internal problem ID [578]
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 5.1 (First order systems and applications). Problems at page 335
Problem number : 13
Date solved : Wednesday, February 05, 2025 at 03:45:50 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=-2 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=2 x \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 1\\ y \left (0\right ) = 0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 15

dsolve([diff(x(t),t) = -2*y(t), diff(y(t),t) = 2*x(t), x(0) = 1, y(0) = 0], 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: 0.002 (sec). Leaf size: 16

DSolve[{D[x[t],t]==-2*y[t],D[y[t],t]==2*x[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*}