b) Solve the differential equation cos 

To solve the given differential equation:

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

we will use the method of integrating factors.

### Step 1: Rearrange the equation to separate the variables y and x.

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

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