The solution of the differential equation `(x^2+1)(dy)/(dx)+(y^2+1)=0` is
a. `y=2+x^2`
b. `y=(1+x)/(1-x)`
c. `y=x(x-1)`
d. `y=(1-x)/(1+x)`

Options

A. `tan^(-1)x-tan^(-1)y=tan^(-1)C`
B. `tan^(-1)y-tan^(-1)x=tan^(-1)C`
C. `tan^(-1)y pm tan^(-1)x=tanC`
D. `tan^(-1)y+tan^(-1)x=tan^(-1)C`

Answer

D

Explanation

If `tan^(-1)y+tan^(-1)x=tan^(-1)C`, then
`(d)/(dx)(tan^(-1)y)+(d)/(dx)(tan^(-1)x)=0`
`rArr" "(1)/(1+y^(2))(dy)/(dx)+(1)/(1+x^(2))=0rArr(1+x^(2))(dy)/(dx)+(1)/(1+y^(2))=0`
Hence, `tan^(-1)x+tan^(-1)y=tan^(-1)C` is the solution of the given differential.