Solve the following initial value problem: `(dy)/(dx)=1+x+y^2+xy^2` when `y=0, x=0`.

Explanation

Given: `frac{d y}{d x}=1+x+y^{2}+x y^{2}`

``
`=frac{d y}{d x}=(1+x)(1+y^{2}) `

`=frac{1}{(1+y^{2})} d y=(1+x) d x`

`=int frac{1}{(1+y^{2})} d y=int(1+x) d x `

`=tan ^{-1} y=x+frac{x^{2}}{2}+C` ………….. ({i})

``
Put `y=0` and `x=0`, then

...