Use the "mixed partials" check to see if the following differential equation is exact. (4x³ + y) dx + (x — 2y) dy = 0. This equation has the form M(x, y) dx + N(x, y) dy = 0. Find: әм მყ -(x, y) = help (formulas) ON -(x, y) = help (formulas) ax If the equation is exact, find a function F(x, y) whose differential, dF(x, y), is the left hand side of the differential equation. That is, the level curves F(x, y) = C are solutions to the differential equation. If the equation is not exact, enter "not exact". F(x, y) = help (formulas) Book: Section 1.8 of Notes on Diffy Qs

Newton’s theory of gravitation states that the weight of a person x feet above sea level is given by:

dy/dx=x-4xy Solve using integrating factor and seperating the variables

Solve the DE y' = y sin x.