Solve: `(1+x^2)(dy)/(dx)+2xy-4x^2=0` subject to the initial condition`y(0)=0.`

Explanation

To solve the differential equation \((1+x^2)\frac{dy}{dx} + 2xy - 4x^2 = 0\) with the initial condition \(y(0) = 0\), we will follow these steps:

### Step 1: Rearrange the Equation
First, we rearrange the equation to isolate \(\frac{dy}{dx}\):
\[ (1+x^2)\frac{dy}{dx} + 2xy = 4x^2 \]
\[
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