For each of the folowing differential equations, find a particular solution satisfying the given condition:
`(dy)/(dx) =-4xy^(2)," it being given that " y = 1 " when " x = 0.`

Answer

`y=(1)/((2x^(2)+1))`

Explanation

`int (dy)/(y^(2))=int -4x dx rArr (-1)/(y) = -2x^(2)+C rArr y = (1)/((2x^(2)-C)) " " `...(i)
Putting x = 0 and y = 1 in (i), we get C = -1.
Hwence, `y = (1)/((2x^(2)+1)).`