\[ \left \{a y(t)+x''(t)=0,y''(t)-a^2 y(t)=0\right \} \] ✓ Mathematica : cpu = 0.0212455 (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 = 0.054 (sec), leaf count = 49
\[ \left \{ \left \{ x \left ( t \right ) ={\frac {-{\it \_C3}\,{{\rm e}^{-at}}-{\it \_C4}\,{{\rm e}^{at}}+a \left ( {\it \_C1}\,t+{\it \_C2} \right ) }{a}},y \left ( t \right ) ={\it \_C3}\,{{\rm e}^{-at}}+{\it \_C4}\,{{\rm e}^{at}} \right \} \right \} \]