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I'm struggling with this concept, cant seem to get my head round it or find any good reference sites or books.

I have calculated the eigen values and eigen vectors for the following matrix

5 3

1 7

Eigen values 4, 8

Eigen vectors 4: 3

-1

Eigen vectors 8: 1

1

Now need to solve these first order coupled differential equations (this is where i just go uhhh?)

dx/dt = 5x + 3y

dy/dt = x + 7y

initial conditions are x(0) = 5 and y(0) = 1

Any help or pointers would be greatly appreciated, my mind has just gone blank.

Thanks Rich (Electronic Engineer - If it aint got wires i cant do it!!)