2.1861   ODE No. 1861

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

$$\{a{x}^{\prime }(t)+b{y}^{\prime }(t)=\alpha x(t)+\beta y(t),b{x}^{\prime }(t)-a{y}^{\prime }(t)=\beta x(t)-\alpha y(t)\}$$ ✓ Mathematica : cpu = 0.0116781 (sec), leaf count = 183

$$\left\{\{x(t)\to c_2{e}^{\frac{t(a\alpha +b\beta )}{a^2+b^2}}\sin \left(\frac{t(a\beta -\alpha b)}{a^2+b^2}\right)+c_1{e}^{\frac{t(a\alpha +b\beta )}{a^2+b^2}}\cos \left(\frac{t(a\beta -\alpha b)}{a^2+b^2}\right),y(t)\to c_2{e}^{\frac{t(a\alpha +b\beta )}{a^2+b^2}}\cos \left(\frac{t(a\beta -\alpha b)}{a^2+b^2}\right)-c_1{e}^{\frac{t(a\alpha +b\beta )}{a^2+b^2}}\sin \left(\frac{t(a\beta -\alpha b)}{a^2+b^2}\right)\}\right\}$$

✓ Maple : cpu = 0.102 (sec), leaf count = 144

$$\left\{\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{(ia\beta -i\alpha b+a\alpha +b\beta )t}{a^2+b^2}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{(ia\beta -i\alpha b-a\alpha -b\beta )t}{a^2+b^2}},y\left(t\right)=i(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{(ia\beta -i\alpha b+a\alpha +b\beta )t}{a^2+b^2}}-\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{(ia\beta -i\alpha b-a\alpha -b\beta )t}{a^2+b^2}})\}\right\}$$