The differential equations, find a particular solution satisfying the given condition: `(1+x^2)(dy)/(dx)+2x y=1/(1+x^2); y=0`when `x = 1`

Explanation

To solve the differential equation \((1+x^2) \frac{dy}{dx} + 2xy = \frac{1}{1+x^2}\) with the initial condition \(y(1) = 0\), we will follow these steps:

### Step 1: Rewrite the Differential Equation
We start by rewriting the given differential equation:
\[ (1+x^2) \frac{dy}{dx} + 2xy = \frac{1}{1+x^2} \]
We can rearrange this to isolate \(\frac{dy}{dx}\):
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