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Linear differental equation of the form ...

Linear differental equation of the form `dy/dx + Py = Q` where P, Q are functions of x or costants and the coefficient of `dy/dx = 1`. Taking `e^(int P dx)` as Integrating factor the above form reduces to `d/dx(ye^(int Pdx))= Qe ^(intPdx).`
Solution of the equation `dy/dx + 2 y tan x = x sin x `given y = 0 when `x = pi/3 ` is -

A

`y = cos x - 2cos^(2) x`

B

`y = sin x - 2 sin ^(2) x`

C

`y = cos x - 2 sin ^(2) sin^(2) x`

D

`y = sin x - 2 cos ^(2) x`

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The correct Answer is:
A
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