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

Options

A. `2 sin^(-1) y = x sqrt(1-y^(2))+c`
B. `sin^(-1) y = (1)/(2) sin^(-1) x + c`
C. `cos^(-1) y = x cos^(-1) x + c`
D. `(1)/(2)"log"((1+y)/(1-y))=x-(x^(3))/(3)+c`

Answer

D

Explanation

`(dy)/(dx) = 1 - x^(2) - y^(2) + x^(2)y^(2)`
`therefore" "(dy)/(dx)=(1-x^(2))(1-y^(2))`
`therefore" "(dy)/(1-y^(2))=(1-x^(2))dx`
`therefore" "int (dy)/(1-y^(2))=int (1-x^(2))dx`
`therefore" "(1)/(2) log((1+y)/(1-y))=x-(x^(3))/(3)+C`