Solve the following IVP.

$x^{\text{'}}(t)=([-2,1],[-5,4])x(t),x(0)=(\frac{2}{1})$

A$.(\frac{\frac{-1}{4}{e}^{3t}+\frac{9}{4}{e}^{-t}}{\frac{-5}{4}{e}^{3t}+\frac{9}{4}{e}^{-t}})$

B$.(\frac{\frac{3}{4}{e}^{3t}+\frac{3}{4}{e}^{-t}}{\frac{-5}{4}{e}^{3t}+\frac{9}{4}{e}^{-t}})$

C$.(\frac{\frac{1}{4}{e}^{3t}+\frac{6}{4}{e}^{-t}}{\frac{1}{4}{e}^{3t}+\frac{9}{4}{e}^{-t}})$

D$.(\frac{\frac{-1}{3}{e}^{3t}+\frac{7}{4}{e}^{-t}}{\frac{-3}{4}{e}^{3t}+\frac{9}{4}{e}^{-t}})$

E$.(\frac{\frac{2}{4}{e}^{3t}+\frac{7}{4}{e}^{-t}}{\frac{-5}{4}{e}^{3t}+\frac{7}{4}{e}^{-t}})$

Handwrting if possible please