Solve the differential equation `x sec^(2) y dy = (xIn x + 1) e^(x) dx`.

Explanation

To solve the differential equation \( x \sec^2 y \, dy = (x \ln x + 1) e^x \, dx \), we will follow these steps:

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

\[ \sec^2 y \, dy = \frac{x \ln x + 1}{x} e^x \, dx \]
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