The solution of the differential equation
` y - x ( dy)/(dx) = a ( y^(2) + dy/dx)` is

Options

A. `y = C (x+a)(1-ay)`
B. `y = C( x+a) (1+ay)`
C. `y = C(x-a)(1+ay)`
D. None of these

Answer

d

Explanation

Given , ` y - x (dy)/(dx) = a (y^(2) +dy/dx)`
` rArr (dy)/(dx) (a+x) = y - ay^(2) `
On integrating both sides , we get
` rArr int (1/y +a/(1-ay))dy = int (dx)/(a+x)`
` rArr log y - log (1-ay) = log (a+x) +log C`
` rArr log y = log (1- ay) (a+x)C`
` rArr y = C ( 1-ay ) (a+x)`