# Homework Help: Exact DE question

1. Dec 11, 2011

### Eastonc2

1. The problem statement, all variables and given/known data
determine whether the DE, (2x+y)dx-(x+6y)dy=0, is exact

2. Relevant equations
i understand how to determine if they are exact, I just don't understand this specific instance. for my case, M(x,y)=2x+y, but would N(x,y)=(x+6y), or (-x-6y)?

3. The attempt at a solution
using my first N(x,y), the equation is exact, however, using the second, they are not exact.

Just need clarification at this point

Last edited: Dec 11, 2011
2. Dec 11, 2011

### I like Serena

Hi Eastonc2!

That is how it matches the definition of an exact DE.

But how did you determine that it was exact with the first N(x,y)?
Because I don't think it is.

3. Dec 11, 2011

### Eastonc2

ah, my fault, M(x,y)=2x+y

i was looking at the equation above it for that first part. the second part is correct though.

4. Dec 11, 2011

### I like Serena

Ah, now I see your dilemma.

To make sure, perhaps you should try to find a function of which the partial derivatives match with M(x,y) and N(x,y).
Can you find such a function?

5. Dec 11, 2011

### LCKurtz

Have you studied the case where M and N are homogeneous of the same degree, as these are?