Question

What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2)  (-2 < y < 2)`

पर्याय

• `y = 2 sin (x + c)`

• `y = 2 cos (x + c)`

• `y = 2 tan (x + c)`

• `2cot (x + c)`

Answer 1

`y = 2 sin (x + c)`

Explanation:

`(dy)/(dx) = sqrt(4 - y^2)` or `(dy)/sqrt(4 - y^2) = dx`

Integrating `int (dy)/sqrt(4 - y^2) = int dx`

`sin^-1  y/2 = x + c` or `y = 2sin (x + c)`