2.1886   ODE No. 1886

\[ \left \{a y(t)+x''(t)=0,y''(t)-a^2 y(t)=0\right \} \] Mathematica : cpu = 0.0144492 (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 = 0.074 (sec), leaf count = 49


\[\left \{x \relax (t ) = \frac {-c_{4} {\mathrm e}^{-a t}-c_{3} {\mathrm e}^{a t}+a \left (t c_{1}+c_{2}\right )}{a}, y \relax (t ) = c_{3} {\mathrm e}^{a t}+c_{4} {\mathrm e}^{-a t}\right \}\]