Q.52. Differential Equation

Question 52.
Solve the differential equation:
(cos(2y)-sin(x))dx-2tan(x)sin(2y)dy=0.

Answer 52.
(cos(2y)-sin(x))dx - 2tan(x)sin(2y)dy = 0
=> cos x cos(2y) dx - sin x cos x dx - 2 sin x sin(2y) dy = 0
=> [cos x cos(2y) dx - 2 sin x sin(2y) dy] - (1/2) sin (2x) dx = 0
=> d [ sin x cos (2y) ] - (1/2) sin (2x) dx = 0

Integrating,
sin x cos (2y) + (1/4) cos (2x) = C'
4sin x cos (2y) + cos (2x) = C

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