The solution of the differential equation `y dx - (x + 2y^2)dy=0` is `x=f(y)`. If `f(-1)=1,` then `f(1)` is equal to

Options

A. 4
B. 3
C. 1
D. 2

Answer

b

Explanation

Given, `y dx = (x - 2y^(2)) dy = 0 `
` rArr ( y dx - x dx)/(y^(2)) = 2dy rArr d ( x/y) = 2dy `
On integrating both sides , we get
` rArr int d(x/y) = 2 int dy `
` rArr x/y = 2y +C`
At x = 1 , y = -1
` :. C = 1 `
Now, ` x/y = 2y +1`
When y = 1 , then f(1) = 3