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Question
What is the general solution of differential equation `(dy)/(dx) = sqrt(4 - y^2) (-2 < y < 2)`
Options
`y = 2 sin (x + c)`
`y = 2 cos (x + c)`
`y = 2 tan (x + c)`
`2cot (x + c)`
MCQ
Solution
`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)`
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