Solve the following differential equation: `y(1-x^2)(dy)/(dx)=x(1+y^2)`

Explanation

To solve the differential equation \( y(1-x^2) \frac{dy}{dx} = x(1+y^2) \), we will use the method of separation of variables. Here’s a step-by-step solution:

### Step 1: Rearranging the Equation
We start by rearranging the given equation to separate the variables \( y \) and \( x \):
\[ y \frac{dy}{dx} = \frac{x(1+y^2)}{1-x^2} \]
Now, we can express this as:
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