dy / dx = sin x / cos y We rewrite the equation: (cos (y) * dy) = (sin (x) * dx) We integrate both sides of the equation: sin (y) = - cos (x) + C We use the initial condition to find the constant C: sin (3pi / 2) = - cos (0) + C -1 = -1 + C C = -1 + 1 C = 0 The equation is then: sin (y) = - cos (x) Clearing y: y = Arcosine (-cos (x)) Answer: An equation for and in terms of x is: y = Arcosine (-cos (x))
