Question

solve the initial value problem using Laplace transform.

x'=-y, y'=4x, x(0)=0, y(0)=0

Answer 1

What is crucial here is to know that the laplace transform of a derivative is sL(y)-y(0) where L is the laplace operator.

Answer 2

so when i take Laplace transform im getting sL(x)-x(0)=-1/s^2 for the first equation and sL(y) -y(0)=4/s^2 for the second i then plug in the values for x(0) and y(0) and get sL(x)=-1/s^2 and sL(y)-1=4/s^2. im not real sure what to do after this.