Solve the following differential equation: `(dy)/(dx)=(cos^2x-sin^2x)cos^2y`

Explanation

To solve the differential equation \(\frac{dy}{dx} = (\cos^2 x - \sin^2 x) \cos^2 y\), we will use the method of separation of variables. Here are the steps:

### Step 1: Separate the variables
We start by rewriting the equation to separate the variables \(y\) and \(x\):

\[ \frac{dy}{\cos^2 y} = (\cos^2 x - \sin^2 x) dx \]
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