The solution of the differential equation `3e^x tan y dx+(1+e^x)sec^2 y dy=0` is

Explanation

To solve the differential equation \( 3e^x \tan y \, dx + (1 + e^x) \sec^2 y \, dy = 0 \), we will use the method of separation of variables. Here’s the step-by-step solution:

### Step 1: Rearranging the Equation
We start by rearranging the given equation to separate the variables \( x \) and \( y \):
\[ 3e^x \tan y \, dx + (1 + e^x) \sec^2 y \, dy = 0 \]
This can be rewritten as:
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