2.1860   ODE No. 1860

1. Problem in Latex
2. Mathematica input
3. Maple input

$$\{x^{\prime }(t)=ax(t)+by(t),y^{\prime }(t)=by(t)+cx(t)\}$$ ✓ Mathematica : cpu = 0.0517421 (sec), leaf count = 362

$$\left\{\{x(t)\to \frac{e^{\frac{1}{2}t(-\sqrt{a^2-2ab+b^2+4bc}+a+b)}(a{c}_1(e^{t\sqrt{a^2-2ab+b^2+4bc}}-1)+c_1\sqrt{a^2-2ab+b^2+4bc}(e^{t\sqrt{a^2-2ab+b^2+4bc}}+1)-b(c_1-2c_2)(e^{t\sqrt{a^2-2ab+b^2+4bc}}-1))}{2\sqrt{a^2-2ab+b(b+4c)}},y(t)\to \frac{e^{\frac{1}{2}t(-\sqrt{a^2-2ab+b^2+4bc}+a+b)}(2c{c}_1(e^{t\sqrt{a^2-2ab+b^2+4bc}}-1)+c_2(a(-e^{t\sqrt{a^2-2ab+b^2+4bc}})+b(e^{t\sqrt{a^2-2ab+b^2+4bc}}-1)+\sqrt{a^2-2ab+b^2+4bc}(e^{t\sqrt{a^2-2ab+b^2+4bc}}+1)+a))}{2\sqrt{a^2-2ab+b(b+4c)}}\}\right\}$$

✓ Maple : cpu = 0.083 (sec), leaf count = 177

$$\left\{\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{t}{2}(a+b+\sqrt{b^2+(-2a+4c)b+a^2})}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{t}{2}(a+b-\sqrt{b^2+(-2a+4c)b+a^2})},y\left(t\right)=\frac{1}{2b}(-\mathit{\_}\mathit{C}\mathit{2}(a-b+\sqrt{b^2+(-2a+4c)b+a^2}){\mathrm{e}}^{\frac{t}{2}(a+b-\sqrt{b^2+(-2a+4c)b+a^2})}-\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{t}{2}(a+b+\sqrt{b^2+(-2a+4c)b+a^2})}(a-b-\sqrt{b^2+(-2a+4c)b+a^2}))\}\right\}$$