Solve the following differential equation: `y (1+e^x)dy=(y+1)e^x dx`

Explanation

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

### Step 1: Rearranging the Equation
We start with the given equation:
\[ y(1 + e^x) dy = (y + 1)e^x dx \]
We can separate the variables by dividing both sides by \( (y + 1)e^x \) and multiplying both sides by \( dy \):
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