# laplace eqn help

• Aug 11th 2008, 12:51 PM
:|max
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
• Aug 12th 2008, 12:21 AM
mr fantastic
Quote:

Originally Posted by :|max
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

Where are you stuck? It would help if you showed your working.

Start with notation .... let LT[x(t)] = X(s) and LT[y(t)] = Y(s), say.

Now take take the Laplace transform of each differential equation.

This gives two linear equations in X(s) and Y(s) that need to be solved simultaneously.

Take the inverse Laplace transform of each resulting solution to get x(t) and y(t).