The solution of differential equation `(1-xy + x^(2) y^(2))dx = x^(2) dy` is

Options

A. tan xy = log |cx|
B. tan (y/x) = tan log |cx|
C. xy = tan log |cx|
D. None of these

Answer

C

Explanation

`(1-xy+x^(2)y^(2))dx = x^(2) dy`
`(1-(xy)+(xy)^(2))dx = x^(2) dy`
Let xy = v.
`y = (v)/(x)`
`therefore" "(dy)/(dx)=(x*(dv)/(dx)-v)/(x^(2))`
`x^(2)dy = xdv - v dx`
So,`" "(1-v+v^(2))dx = xdv - vdx`
`rArr" "(1+v^(2))dx = xdv`
`rArr" "int (dv)/(1+v^(2))=int(dx)/(x)`
`rArr" "tan^(-1)v=log|x|+log c`
`rArr" "tan^(-1)v = log |cx|`
`rArr" "v = tan log |cx|`
`rArr" "xy = tan log |cx|`