Question

Ordinary differential equation problem:

(3x^2 + 3e^xsin(y))dy + (x^3cot(y) + 6e^xcos(y))dy = 0

It is not exact obviously so I found the a multiplication factor μ(x) = sin(y)

see:
imgur.com/OC9AZcN

I'm stuck because I can't find g(x) after integrating My(x,y), I keep getting y terms in it see:
http://imgur.com/4BSNwxa

Any help would be greatly appreciated this problem is making me crazy

Answer 1

Anyone see a way algebraically to cancel out the x terms in the last expression?

Answer 2

I checked all my math and have done the problem both ways you can do it and I still end up with a wonky g(x) or g(y)

Answer 3

I'm just trying to solve for g'(y) so that it only contains y terms

Answer 4

question: you find out \(\dfrac{\partial M}{\partial y}=\dfrac{\partial M}{\partial x}\)
so it is exact , why did you say it is not exact?

Answer 5

You need to check if the partial derivative of M in respect to y = the partial derivative of N with respect to x

Answer 6

to see if it is exact

Answer 7

I think I know what I did I'm messing up the second part of the problem finding g(x)/g(y)

Answer 8

I know the concept, just wonder, the given equation is already exact, what are you looking for?

Answer 9

The given equation isn't exact, if you do the partial derivatives you get
M_y(x,y) = 3(e^x)cos(x)
N_x(x,y) = 3x^2cot(y) + 6e^x(cos(y))
M_y(x,y) =/= N_x(x,y) therefore the given equation is not exact
hence why I determined a multiplication factor to make it exact

I messed up the second part of the question, I didn't integrate the right thing to find the g(x) term. I fixed it though and I should be fine.

Answer 10

This is the way I learned it maybe you have a better knowledge of these things.