\[ \left \{x'(t)=a y(t),y'(t)=b x(t)\right \} \] ✓ Mathematica : cpu = 0.0077861 (sec), leaf count = 182
DSolve[{Derivative[1][x][t] == a*y[t], Derivative[1][y][t] == b*x[t]},{x[t], y[t]},t]
\[\left \{\left \{x(t)\to \frac {1}{2} c_1 e^{-\sqrt {a} \sqrt {b} t} \left (e^{2 \sqrt {a} \sqrt {b} t}+1\right )+\frac {\sqrt {a} c_2 e^{-\sqrt {a} \sqrt {b} t} \left (e^{2 \sqrt {a} \sqrt {b} t}-1\right )}{2 \sqrt {b}},y(t)\to \frac {\sqrt {b} c_1 e^{-\sqrt {a} \sqrt {b} t} \left (e^{2 \sqrt {a} \sqrt {b} t}-1\right )}{2 \sqrt {a}}+\frac {1}{2} c_2 e^{-\sqrt {a} \sqrt {b} t} \left (e^{2 \sqrt {a} \sqrt {b} t}+1\right )\right \}\right \}\] ✓ Maple : cpu = 0.062 (sec), leaf count = 64
dsolve({diff(x(t),t) = a*y(t), diff(y(t),t) = b*x(t)})
\[\left \{x \left (t \right ) = c_{1} {\mathrm e}^{\sqrt {a}\, \sqrt {b}\, t}+c_{2} {\mathrm e}^{-\sqrt {a}\, \sqrt {b}\, t}, y \left (t \right ) = \frac {\sqrt {b}\, \left (c_{1} {\mathrm e}^{\sqrt {a}\, \sqrt {b}\, t}-c_{2} {\mathrm e}^{-\sqrt {a}\, \sqrt {b}\, t}\right )}{\sqrt {a}}\right \}\]