Internal problem ID [10182]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1859.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=a x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+a y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 37
dsolve({diff(x(t),t)=a*x(t)-y(t),diff(y(t),t)=x(t)+a*y(t)},singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{a t} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \\ y \left (t \right ) &= {\mathrm e}^{a t} \left (c_{2} \sin \left (t \right )-c_{1} \cos \left (t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 43
DSolve[{x'[t]==a*x[t]-y[t],y'[t]==x[t]+a*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{a t} (c_1 \cos (t)-c_2 \sin (t)) \\ y(t)\to e^{a t} (c_2 \cos (t)+c_1 \sin (t)) \\ \end{align*}