The general solution of
`y^(2)dx+(x^(2)-xy+y^(2))dy=0`, is

Options

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

Answer

A

Explanation

Given, `(dx)/(dy)+((x)/(y))^(2)-((x)/(y))+1=0`
Put `x=(x)/(y)impliesx=vy`
`implies(dx)/(dy)=v+y(dv)/(dy)`
`thereforev+y(dv)/(dy)+v^(2)-v+1=0`
`implies(dv)/(v^(2)+1)+(dy)/(y)=0`
`impliestan^(-1)v+logy+c=0` [intergrating]
`impliestan^(-1)(x)/(y)+logy+c=0`