Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function (x, y) whose differential, d(x, y) gives the differential equation. That is, level curves F(x, y)=C are solutions to the differential equation:
dy/dx = −3x^4 + 2y / − 2x − 4y^2
First rewrite as (x, y)dx + (x, y)dy = 0 where (x, y) = , and (x, y)= . If the equation is not exact, enter not exact, otherwise enter in (x, y) as the solution of the differential equation here = .

The correct question is:

Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose differential, dF(x,y) gives the differential equation. That is, level curves F(x,y) = C are solutions to the differential equation:

dy/dx = (-3x^4 + 2y)/(-2x - 4y^2).

First rewrite as M(x,y)dx + N(x,y)dy = 0 where M(x,y) = -3x^4 + 2y, and N(x,y) = 2x + 4y^2).

If the equation is not exact, enter not exact, otherwise enter in F(x,y) as the solution of the differential equation

F(x, y) = 2(x + y)

Step-by-step explanation:

Given

M(x,y) = -3x^4 + 2y, and N(x,y) = 2x + 4y^2).

Suppose the differential equation is exact, then

∂N/∂x = ∂M/∂y

∂N/∂x = 2, and ∂M/∂y = 2

Therefore the equation is exact.

The solution F(x, y) can be obtained by integrating ∂M/∂y and ∂N/∂x

Integral of ∂M/∂y is 2y + f(x)

Integral of ∂N/∂x is 2x + f(y)

F(x, y) = 2(x + y).

For arbitrary constants f(x) = f(y) = 0

step-by-step explanation:

the answer is 489

step-by-step explanation: