7.22.4 problem 14

Internal problem ID [579]
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 : 14
Date solved : Wednesday, February 05, 2025 at 03:45:51 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=10 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=-10 x \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 3\\ y \left (0\right ) = 4 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 33

dsolve([diff(x(t),t) = 10*y(t), diff(y(t),t) = -10*x(t), x(0) = 3, y(0) = 4], singsol=all)
 

\begin{align*} x \left (t \right ) &= 4 \sin \left (10 t \right )+3 \cos \left (10 t \right ) \\ y \left (t \right ) &= 4 \cos \left (10 t \right )-3 \sin \left (10 t \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 34

DSolve[{D[x[t],t]==10*y[t],D[y[t],t]==-10*x[t]},{x[0]==3,y[0]==4},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 4 \sin (10 t)+3 \cos (10 t) \\ y(t)\to 4 \cos (10 t)-3 \sin (10 t) \\ \end{align*}