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Derivative of Some Standard Functions

If 2+sin x d ...

Question

If (2+sinx)dy/dx + (y+1)cosx = 0 and y(0) = 0 then y(π/2) is equal to

A) -1/3. B) 4/3. C)1/3. D)-2/3

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Solution

(2 + sin x)dy + cos x(y + 1)dx = 0 (y + 1)(2 + sin x) = C (1 + 1)(2 + 0) = C = 4 (y + 1)(2 + sin x) = 4 Put x =π/2 y = 1/3 The correct option is A.

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