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

Explanation

To solve the differential equation \((1+y^2)dx=(\tan^{-1}y-x)dy\), we will follow these steps:

### Step 1: Rearranging the Equation
We start by rewriting the given equation in the form of \(\frac{dx}{dy}\):
\[ (1+y^2)dx = (\tan^{-1}y - x)dy \]
Dividing both sides by \(dy\) and \(1+y^2\), we get:
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