Internal problem ID [12208]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 3, SYSTEMS OF DIFFERENTIAL EQUATIONS. Problems page
209
Problem number: Problem 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 0, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve([diff(x(t),t) = y(t), diff(y(t),t) = -x(t), x(0) = 0, y(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= \sin \left (t \right ) \\ y \left (t \right ) &= \cos \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[{x'[t]==y[t],y'[t]==-x[t]},{},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (t)+c_2 \sin (t) \\ y(t)\to c_2 \cos (t)-c_1 \sin (t) \\ \end{align*}