Solve the differential equation `(dy)/(dx)=1+x+y^(2)+xy^(2)`, when y=0 and x=0.

Explanation

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

### Step 1: Rewrite the equation
We start with the given differential equation:
\[ \frac{dy}{dx} = 1 + x + y^2 + xy^2 \]
We can rearrange the right-hand side by factoring out common terms. Notice that \(y^2\) can be factored:
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