Show that the differential equation of which `y=2(x^2-1)+c e^(-x^2)` is a solution, is `(dy)/(dx)+2x y=4x^3dot`

Explanation

To show that the differential equation \( \frac{dy}{dx} + 2xy = 4x^3 \) has the solution \( y = 2(x^2 - 1) + c e^{-x^2} \), we will follow these steps:

### Step 1: Differentiate \( y \)
Given:
\[ y = 2(x^2 - 1) + c e^{-x^2} \]
We need to find \( \frac{dy}{dx} \).
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