The document describes the process of finding the general solution in implicit form of the given differential equation using separation of variables. It demonstrates the separation of variables leading to an integral equation. The final expression after integration shows a relationship between x and y involving trigonometric functions.

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