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.)

Determine if the following statement is true or false. the normal curve is symmetric about its​ mean, mu. choose the best answer below. a. the statement is false. the normal curve is not symmetric about its​ mean, because the mean is the balancing point of the graph of the distribution. the median is the point where​ 50% of the area under the distribution is to the left and​ 50% to the right.​ therefore, the normal curve could only be symmetric about its​ median, not about its mean. b. the statement is true. the normal curve is a symmetric distribution with one​ peak, which means the​ mean, median, and mode are all equal.​ therefore, the normal curve is symmetric about the​ mean, mu. c. the statement is false. the mean is the balancing point for the graph of a​ distribution, and​ therefore, it is impossible for any distribution to be symmetric about the mean. d. the statement is true. the mean is the balancing point for the graph of a​ distribution, and​ therefore, all distributions are symmetric about the mean.