Consider the following differential equation. (sin(y) – y sin(x)) dx + (cos(x) + x cos(y) - y) dy = 0 Let M = sin(y) – y sin(x) and N = cos(x) + x cos(y) – y. Find the following partial derivatives. My = cos y – sin(x) Nx = -sin (x) + cos(y) = sin(y) – y sin(x). Integrate each term of this partial derivative with respect to x, letting h(y) be an unknown function in y. f(x, y) = x sin(y) + y cos(x) + hy) Find the derivative of h(y). h'(Y) = -cos(y) – cos(x) Is the given differential equation exact?
yes
no
Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.)