Internal problem ID [10180]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1857.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=a y \left (t \right )\\ y^{\prime }\left (t \right )&=-a x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve({diff(x(t),t)=a*y(t),diff(y(t),t)=-a*x(t)},singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (a t \right )+c_{2} \cos \left (a t \right ) \\ y \left (t \right ) &= \cos \left (a t \right ) c_{1} -\sin \left (a t \right ) c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 39
DSolve[{x'[t]==a*y[t],y'[t]==-a*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 \cos (a t)+c_2 \sin (a t) \\ y(t)\to c_2 \cos (a t)-c_1 \sin (a t) \\ \end{align*}