Solution of the equation
`xdy=(y+(xf(y//x))/(f'(y//x)))` dx is-

Options

A. `absf(y//x)=cabs(x),cinR`
B. `absf(y//x)=abs(x)+c,cgt0`
C. `absf(y//x)=cabs(x),cgt0`
D. None of these

Answer

3

Explanation

`(dy)/(dx)= (y)/(x) +(f(y//x))/(f(y//x))" "...(i)`
Let `(y)/(x) = v `
`v+ x(dv)/(dx) = v + (f(v))/(f(v)) " "," "int(f(v))/(f(v)) dv = int (dx)/(x)`
`rArrIn |f(y//x) |=In|x|+ Inc`
`rArr f(y//x)|=c|x|, ` where `cgt 0`