\[ \boxed { \left \{ {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) +ay \left ( t \right ) =0,{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y \left ( t \right ) -{a}^{2}y \left ( t \right ) =0 \right \} } \]
Mathematica: cpu = 0.021003 (sec), leaf count = 115 \[ \left \{\left \{x(t)\to -\frac {c_4 e^{-a t} \left (-2 a t e^{a t}+e^{2 a t}-1\right )}{2 a^2}-\frac {c_3 e^{-a t} \left (e^{a t}-1\right )^2}{2 a}+c_2 t+c_1,y(t)\to \frac {1}{2} c_3 e^{-a t} \left (e^{2 a t}+1\right )+\frac {c_4 e^{-a t} \left (e^{2 a t}-1\right )}{2 a}\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 50 \[ \left \{ \left \{ x \left ( t \right ) =-{\frac {-{\it \_C1}\,ta+{\it \_C3}\,{{\rm e}^{at}}+{\it \_C4}\,{{\rm e}^{-at}}-{\it \_C2}\,a}{a}},y \left ( t \right ) ={\it \_C3}\,{{\rm e}^{at}}+{\it \_C4}\,{{\rm e}^{-a t}} \right \} \right \} \]