laplace eqn help

:|

Hey can anyone tell me the method to solve this, I can do inverse linear eqns and such but i dont know how to solve this type of question:


Use Laplace transforms to solve the following systems of linear equations

(a) dx/dt= 3x(t) − 4y(t),
dy/dt= 2x(t) + 3y(t),

with initial conditions x(0) = 1, y(0) = 0.


thanks

Michael Collins

The 1st one:

dx/dt = 3 x(t) - 4 y(t)

So now take Laplace Transform (differentiation corresponds to multiplication by s in the Laplace domain, then minus the initial condition):

s X(s) - x(0) = 3 X(s) - 4 Y(s)
s X(s) - 1 = 3 X(s) - 4 Y(s)
s X(s) - 3 X(s) = 1 - 4 Y(s)
X(s) [s - 3] = 1 - 4 Y(s)
X(s) = 1/(s - 3) - 4 Y(s) / (s - 3)

Now solve the 2nd one in the same way, to get an expression for Y(s), sub this into the above, then take the inverse Laplace Transform.

:|

got it out, thanks for your help