\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =ay \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =bx \left ( t \right ) \right \} } \]
Mathematica: cpu = 0.010501 (sec), leaf count = 182 \[ \left \{\left \{x(t)\to \frac {1}{2} c_1 e^{-\sqrt {a} \sqrt {b} t} \left (e^{2 \sqrt {a} \sqrt {b} t}+1\right )+\frac {\sqrt {a} c_2 e^{-\sqrt {a} \sqrt {b} t} \left (e^{2 \sqrt {a} \sqrt {b} t}-1\right )}{2 \sqrt {b}},y(t)\to \frac {\sqrt {b} c_1 e^{-\sqrt {a} \sqrt {b} t} \left (e^{2 \sqrt {a} \sqrt {b} t}-1\right )}{2 \sqrt {a}}+\frac {1}{2} c_2 e^{-\sqrt {a} \sqrt {b} t} \left (e^{2 \sqrt {a} \sqrt {b} t}+1\right )\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 64 \[ \left \{ \left \{ x \left ( t \right ) ={\it \_C1}\,{{\rm e}^{\sqrt {a} \sqrt {b}t}}+{\it \_C2}\,{{\rm e}^{-\sqrt {a}\sqrt {b}t}},y \left ( t \right ) ={1\sqrt {b} \left ( {\it \_C1}\,{{\rm e}^{\sqrt {a}\sqrt {b}t }}-{\it \_C2}\,{{\rm e}^{-\sqrt {a}\sqrt {b}t}} \right ) {\frac {1}{ \sqrt {a}}}} \right \} \right \} \]