Solve the system of differential equations

$\{\begin{array}{c}{x}^{\text{'}}=197x+52y\end{array}$

$y^{\text{'}}=-735x-194y$

$x(0)=-14,y(0)=53$

The lesser of the two eigenvalues is $1$

Its corresponding eigevector is $\left[\begin{array}{c}-13\\ 49\end{array}\right].$

The greater of the two eigenvalues is $2$

Its corresponding eigevector is $\left[\begin{array}{c}-4\\ 15\end{array}\right].$

The solution to the system is

$x(t)=$

$y(t)=$