The solution of the differential equation
`(dy)/(dx) = y tan x - 2 sin x`, is

Options

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

Answer

b

Explanation

Given , ` (dy)/(dx) + (2x)/(1+x^(2))*y = 1/(1+x^(2))^(2)`
` :' IF = e^(int (2x)/(1+x^(2)dx))= e^(log (1+x^(2)) =) = 1+x^(2)`
` :. ` General soultion is
` y (1+x^(2)) = int (1+x^(2) )* 1/(1+x^(2))^(2) dx +C`
` rArr y (1+x^(2))= tan^(-1) x +C`