The solution of the differential equation `(1+y^(2)) tan^(-1) x dx + y(1+x^(2)) dy = 0` is

Options

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

Answer

b

Explanation

Given differential equation is
` (1+y^(2)) tan^(-1) x dx + y ( 1+x^(2)) dy = 0`
` rArr (tan^(-1)x)/(1+x^(2)) dx + y/(1+y^(2)) dy = 0`
On integrating both sides we get
` rArr ((tan^(-1)x)^(2))/2 + 1/2 log (1+y^(2)) = C/2 `
` rArr log (1+y^(2) ) + (tan^(-1)x)^(2) = C`