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find the general solution in implicit form of the differential equation csc y dx + sec^2 x dy = 0 by
separation of variables
Solution
dx/siny + dy/cos2(x) = 0
dx/siny =-dy/cos2(x)
dx cos2(x) = -dy siny
(1+cos2x)/2 dx = -siny dy
integrate on both sides
x/2 + sin(2x)/4 = cos(y) + C

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find the general solution in implicit form of the differential equat.pdf

  • 1. find the general solution in implicit form of the differential equation csc y dx + sec^2 x dy = 0 by separation of variables Solution dx/siny + dy/cos2(x) = 0 dx/siny =-dy/cos2(x) dx cos2(x) = -dy siny (1+cos2x)/2 dx = -siny dy integrate on both sides x/2 + sin(2x)/4 = cos(y) + C