The differential equation dy/dx = M(x, y) / N(x, y) is exact if _______.

If dy/dx = 8y²x³ and y(2) = 1, then 1/y(0) (in integer) is _______.

Let y' and y'' denote the first and second order derivatives of y with respect to x, respectively. Let y(x) be a solution of the initial value problem: y'' - 3y...