2.1859   ODE No. 1859

\[ \left \{x'(t)=a x(t)-y(t),y'(t)=a y(t)+x(t)\right \} \] Mathematica : cpu = 0.0044125 (sec), leaf count = 51


\[\left \{\left \{x(t)\to c_1 e^{a t} \cos (t)-c_2 e^{a t} \sin (t),y(t)\to c_2 e^{a t} \cos (t)+c_1 e^{a t} \sin (t)\right \}\right \}\] Maple : cpu = 0.047 (sec), leaf count = 37


\[\{x \relax (t ) = {\mathrm e}^{a t} \left (c_{1} \sin \relax (t )+c_{2} \cos \relax (t )\right ), y \relax (t ) = {\mathrm e}^{a t} \left (\sin \relax (t ) c_{2}-\cos \relax (t ) c_{1}\right )\}\]