The solution of differential equation
`(xy^(5)+2y)dx-xdy =0,` is

Options

A. `9 x^(8) + 4x^(9) y^(4) = 9y^(4)C`
B. ` 9x^(8) - 4x^(9) y^(4) - 9y^(4) C = 0 `
C. ` x^(8) (9+4y^(4)) = 10y^(4)C`
D. None of these

Answer

a

Explanation

`(xy^(5)+2y)dx = xdy`
` rArr x (dy)/(dx) - 2y = xy^(5)`
` rArr (dy)/(dx) -(2y)/x = y^(5)`
` rArr y^(-5) (dy)/(dx) - (2y^(-4))/x = 1" "` …(i)
Put , `y^(-4) =t`
` rArr -4y^(-5) (dy)/(dx) = (-1)/4 (dt)/(dx)" "` …(ii)
From Eqs. (i) and (ii) ,
` -1/4 (dt)/(dx) - (2t)/x = 1 rArr (dt)/(dx) + (8t)/x =-4`
` IF = e^(int 8/xdx) = e^(8logx) = x^(8)`
` :. t* x^(8) int (-4)x^(8) dx +C`
` rArr (x^(8))/(y^(4))= -(4*x^(9))/9 +C`
` rArr 9x^(8) + 4x^(9)* y^(4) = 9y^(4)C`