The differential equations, find a particular solution satisfying the given condition: `(dy)/(dx)=ytanx ; y=1`when x = 0

Explanation

To solve the differential equation \(\frac{dy}{dx} = y \tan x\) with the initial condition \(y = 1\) when \(x = 0\), we will use the method of separation of variables. Here’s a step-by-step solution:

### Step 1: Separate the variables
We start with the differential equation:
\[ \frac{dy}{dx} = y \tan x \]
We can rearrange this to separate the variables \(y\) and \(x\):
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