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:

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

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im not sure