In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y)=C, give implicit general solutions to the differential equation. If the equation is not exact, enter NE otherwise find F(x, y) (note you are not asked to enter C) F(x, y)= NE

Step-by-step explanation:

Let:

This is and exact equation, because:

So, define f(x,y) such that:

The solution will be given by:

Where C1 is an arbitrary constant

Integrate with respect to x in order to find f(x,y):

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

Substitute into

Integrate with respect to y:

Substitute g(y) into f(x,y):

The solution is f(x,y)=C1

Solving y using quadratic formula:

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.