Use Laplace transform to solve the system

Question

$\frac{\partial x}{\partial t} = -y$ , $\frac{\partial y}{\partial t} = x.$

For $t\geq 0$ , with $x(0) = 1$, $y(0) = 0$.

I have no clue on how to start the question. Could some please give me a lead.

The answer is $x(t) = \cos(t)$ and $y(t) = \sin(t)$

Answer 1

Hint Solving with out using Laplace transformation (if you are allowed):
we have $ x''(t)=-y'(t)=-x(t)$ and so your equation is $x''(t)+x(t)=0$ It is a lnear homogenous differential equation second order with constant coeffitients. You can use this site to find the solution.