If `y(x)` is the solution of the differential equation `(dy)/(dx)=-2x(y-1)` with `y(0)=1`, then `lim_(xrarroo)y(x)` equals

Options

A. `0`
B. `1`
C. `e`
D. `oo`

Answer

B

Explanation

`(dy)/(dt)=-2x(y-1)`
`(dy)/(dx)+2x=2x, I.F.=e^(int(2xdx)=e^(x^(2))`
solution `impliesy.e^(x^(2))=int2xe^(x^(2))dx+c`
`y.e^(x^(2))+c`……….(1)
Given `Y(0)=1implies1,1=1+cimplies0`
`:.y.e^(x^(2))=e^(x^(2))` (from 1)
`y=1`
`:.lim_(xrarroo)y(x)=lim_(xrarroo)(1)=1`