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x(dy)/(dx)+2y=x cos x...

x(dy)/(dx)+2y=x cos x

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Solve (dy)/(dx)+2y=cos x.

Solve (dy)/(dx)+2y=cos x.

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(dy) / (dx) -y cos x = 2x sin x

cos ^ (3) x (dy) / (dx) + y cos x = sin x

The solution of (dy)/(dx) + y cos x = sin x cos x is

Solution of the differential equation 2 y sin x (dy)/(dx) = 2 sin x cos - y^(2) cos x satisfying y(pi//2) = 1 is given by

(x + y (dy) / (dx)) / (yx (dy) / (dx)) = (x cos ^ (2) (x ^ (2) + y ^ (2))) / (y ^ ( 3))