Answer: Determine whether each of the equations in 1 through 8 is exact. If it is exact

Chapter 2, Problem 3

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QUESTION:

Determine whether each of the equations in 1 through 8 is exact. If it is exact, find the solution. (3x2 2xy + 2) + (6y2 x2 + 3) y_ = 0

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QUESTION:

Determine whether each of the equations in 1 through 8 is exact. If it is exact, find the solution. (3x2 2xy + 2) + (6y2 x2 + 3) y_ = 0

ANSWER:

Step 1 of 2

The given differential equation is

Rewriting the differential equation as,

Now, a differential equation of the form  is called exact D.E if

 

Comparing the differential equations we have,

 

Differentiating partially M and N with respect to x and y,

 

So,

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