How Do You Solve Differential Equations Using Integration by Quadratures?

[Reid]

Homework Statement

I cannot get my head around these equations...
$$\dot{x}(t)=-sin y(t)$$

$$\dot{y}(t)=-\frac{cos x(t)}{sin x(t)} cos y(t).$$

They are to be solved with integration by quadratures. :S But I am not at all familiar with that technique and I can't find any tutorial for it.

Since I have never heard about it before i can't make an attempt either! :(

 

[chaoseverlasting]

http://mathworld.wolfram.com/Quadrature.html

I don't know what exactly you need, but I am guessing you differentiate your first equation wrt t and substitute the result in the second equation to get an equation in one variable which you solve, and then use that result to find the solution for the remaining variable.