Solve: x*cot(y) = dy/dx*sec(x) = 0

-dy/dx*sec(x) = -x*cot(y)

dy/dx*sec(x) = x*cot(y)

dy/cot(y) = x*dx/(sec(x))

integration

-ln|cos(y)| = x*sin(x) + cos(x) + C

ln|cos(y)| = -x*sin(x) - cos(x) + A

cos(y) = e^(-x*sin(x) - cos(x) + A)

y = arccos(e^(-x*sin(x) - cos(x))+ A

Is it correct and can I write this better? Thanks.