The general solution of `(dy)/(dx)=2xe^(x^(2)-y)` is

Options

A. `e^(x^(2)-y)=C`
B. `e^(-y)+e^(x^(2))=C`
C. `e^(y)+e^(x^(2))+C`
D. `e^(x^(2)+y)=C`

Explanation

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

### Step 1: Rearranging the Equation
We start by rewriting the equation:
\[ \frac{dy}{dx} = 2x e^{x^2} e^{-y} \]
This can be rearranged to:
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