Find the particular solution of the differential equation `(dy)/(dx)=-4x y^2` given that `y" "=" "1` , when`x" "=" "0` .

Explanation

From the given equation

`frac{d y}{ d x}=-4 x y^{2} `

`int\frac{d y}{ d x}=\int-4 x d x `

`-1 / y^{2}=-4 \cdot(x^{2} / 2)+c `

`-(1 / y)=-2 x^{2}+c `

`2 x^{2}-(1 / y)-c=0 \ldots \text { (i) } `


`y=1 \text { and } x=0


...