Find the general solution implicit if necessary explicit if

Find the general solution (implicit if necessary, explicit if convenient) for the following: secx dy / = csc y Verify that the differential equation is exact, then solve it. (4x - y) dx + (6y - x)dy = 0

Solution

siny dy = cisx dx -cosy = sinx + c (4x-y) dx + (6y-x)dy = 0 M dx + N dy = 0 DM/dy = -1 DN/dx = -1 EXACT form !!! integrate M wrt x : 2x*x - yx + f(y) itegrate N wrt y : 3y*y - xy + g(x) compairing both eq : 3y*y + 2x*x - xy answer !!!