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(dy)/(dx) + y=1, y ne 1...

`(dy)/(dx) + y=1, y ne 1`

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If y^x=x^y then (dy)/(dx) at x=1, y=1 is

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

Solution of (dy)/(dx) = (x)/(y) (y ne 0) is

x(dy/dx + y ) = 1 -y

cos ((dy)/(dx)) = a (a ne R), y = 1 when x = 0

cos ((dy)/(dx)) = a (a ne R), y = 1 when x = 0