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Question

dydx=1-cos x1+cos x

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Solution

We have, dydx=1-cos x1+cos xdydx=2sin2 x22cos2 x2dydx=tan2 x2dy=tan2 x2dxIntegrating both sides, we getdy=tan2 x2dxdy=sec2 x2-1dxy= 2 tan x2-x+CSo, y= 2 tan x2-x+C is defined for all xR. Hence, y= 2 tan x2-x+C, where xR, is the solution to the given differential equation.

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