The general solution of the differential equation `(dx)/(dy)+(x/y)^2-(x/y)+1=0` is

Options

A. ` tan^(-1) (x/y) + log y + C = 0`
B. `2 tan^(-1) (x/y) + log x + C = 0 `
C. ` log (y+sqrt(x^(2)+y^(2)))+log y +c = 0`
D. ` sin^(-1) (x/y) + log y +C = 0`

Answer

a

Explanation

Given , ` (dy)/(dx) +(x/2)^(2) -(x/y) +1=0`
Put `v = x/2 rArr x = vy`
` rArr (dx)/(dy) = v+y (dv)/(dy)`
` :. v + y (dy)/(dy) +v^(2) - v +1=0`
` rArr (dv)/(v^(2)+1)+(dy)/(y)=0`
`rArr v + y (dv)/(dy) +v^(2) - v+1 = 0`
` tan ^(-1) v + log y + C = 0` [ integrating ]
` rArr tan^(-1) x/y + log y + C = 0`