\[ \left \{x'(t)=a x(t)+b y(t),y'(t)=b y(t)+c x(t)\right \} \] ✓ Mathematica : cpu = 0.0348163 (sec), leaf count = 696
\[\left \{\left \{x(t)\to \frac {c_1 \left (a \left (-e^{\frac {1}{2} t \left (-\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}\right )+a e^{\frac {1}{2} t \left (\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}+b e^{\frac {1}{2} t \left (-\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}+\sqrt {a^2-2 a b+b^2+4 b c} e^{\frac {1}{2} t \left (-\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}-b e^{\frac {1}{2} t \left (\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}+\sqrt {a^2-2 a b+b^2+4 b c} e^{\frac {1}{2} t \left (\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}\right )}{2 \sqrt {a^2-2 a b+b^2+4 b c}}-\frac {b c_2 \left (e^{\frac {1}{2} t \left (-\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}-e^{\frac {1}{2} t \left (\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}\right )}{\sqrt {a^2-2 a b+b^2+4 b c}},y(t)\to \frac {c_2 \left (a e^{\frac {1}{2} t \left (-\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}-a e^{\frac {1}{2} t \left (\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}-b e^{\frac {1}{2} t \left (-\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}+\sqrt {a^2-2 a b+b^2+4 b c} e^{\frac {1}{2} t \left (-\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}+b e^{\frac {1}{2} t \left (\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}+\sqrt {a^2-2 a b+b^2+4 b c} e^{\frac {1}{2} t \left (\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}\right )}{2 \sqrt {a^2-2 a b+b^2+4 b c}}-\frac {c c_1 \left (e^{\frac {1}{2} t \left (-\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}-e^{\frac {1}{2} t \left (\sqrt {a^2-2 a b+b^2+4 b c}+a+b\right )}\right )}{\sqrt {a^2-2 a b+b^2+4 b c}}\right \}\right \}\] ✓ Maple : cpu = 0.102 (sec), leaf count = 177
\[\left \{\left \{x \left (t \right ) = c_{1} {\mathrm e}^{\frac {\left (a +b +\sqrt {a^{2}+b^{2}+\left (-2 a +4 c \right ) b}\right ) t}{2}}+c_{2} {\mathrm e}^{\frac {\left (a +b -\sqrt {a^{2}+b^{2}+\left (-2 a +4 c \right ) b}\right ) t}{2}}, y \left (t \right ) = \frac {-c_{1} \left (a -b -\sqrt {a^{2}+b^{2}+\left (-2 a +4 c \right ) b}\right ) {\mathrm e}^{\frac {\left (a +b +\sqrt {a^{2}+b^{2}+\left (-2 a +4 c \right ) b}\right ) t}{2}}-c_{2} \left (a -b +\sqrt {a^{2}+b^{2}+\left (-2 a +4 c \right ) b}\right ) {\mathrm e}^{\frac {\left (a +b -\sqrt {a^{2}+b^{2}+\left (-2 a +4 c \right ) b}\right ) t}{2}}}{2 b}\right \}\right \}\]