The following simultaneous ordinary differential equations present a mathematical model for a

system:

x$^()+4$x$^()-5$y$^()-3$x$^()+4$y$^()+6$y$^()+10$y$-7$x$=3$

y$^()+2$y$^()-5$x$^()+$y$^()+4$x$^()+10$y$-7$x$=-1$

Considering that the initial conditions are all zeros.

Present these differential equations in a state space equation.

Solve the state space equation, and plot the variations of x and y versus time for the range of $0<=<=$t$<=5$ seconds.

Also, plot the variations of x$^()$ and y$^()$ versus time for the range of $0<=<=$t$<=5$ seconds.

Determine the roots of the characteristic equation for the presented system.

Using Routh's Criterion to determine the system's stability.

Explain if the results from items $4$ and $5$ support each other.