Solve: `(dy)/(dx)=ysin2x` it being given that `y(0)=1.`

Explanation

To solve the differential equation \(\frac{dy}{dx} = y \sin(2x)\) with the initial condition \(y(0) = 1\), we will follow these steps:

### Step 1: Separate Variables
We start by separating the variables \(y\) and \(x\):
\[ \frac{dy}{y} = \sin(2x) \, dx \]

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