Internal problem ID [9436]
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 }\relax (t )&=a y \relax (t )\\ y^{\prime }\relax (t )&=-a x \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.076 (sec). Leaf size: 35
dsolve({diff(x(t),t)=a*y(t),diff(y(t),t)=-a*x(t)},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = c_{1} \sin \left (a t \right )+c_{2} \cos \left (a t \right ) \] \[ y \relax (t ) = \cos \left (a t \right ) c_{1}-\sin \left (a t \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.006 (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*}