\[ \left \{a y(t)+x''(t)=0,y''(t)-a^2 y(t)=0\right \} \] ✓ Mathematica : cpu = 0.0219043 (sec), leaf count = 103
\[\left \{\left \{x(t)\to \frac {c_4 \left (2 a t+e^{-a t}-e^{a t}\right )}{2 a^2}-\frac {c_3 e^{-a t} \left (e^{a t}-1\right )^2}{2 a}+c_2 t+c_1,y(t)\to \frac {e^{-a t} \left (a c_3 \left (e^{2 a t}+1\right )+c_4 \left (e^{2 a t}-1\right )\right )}{2 a}\right \}\right \}\]
✓ Maple : cpu = 0.065 (sec), leaf count = 49
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {-{\it \_C4}\,{{\rm e}^{-at}}-{\it \_C3}\,{{\rm e}^{at}}+a \left ( {\it \_C1}\,t+{\it \_C2} \right ) }{a}},y \left ( t \right ) ={\it \_C3}\,{{\rm e}^{at}}+{\it \_C4}\,{{\rm e}^{-at}} \right \} \right \} \]