# Thread: integrating factor

1. ## integrating factor

is my integral R(x) and R(y) correct ? why it look so complicated ?

2. ## Re: integrating factor

Neither are integrating factors because they are not expressions in a single variable. Can you post the full text of the question?

3. ## Re: integrating factor

Originally Posted by Archie
Neither are integrating factors because they are not expressions in a single variable. Can you post the full text of the question?
the full text is Show that the first order differential equation is EXACT equation . (sin x - x sin y) dx + (cos y + y cos x ) dy = 0

4. ## Re: integrating factor

Perhaps the differentials are transposed. The following is exact:
$$(\sin x - x\sin y) \,\mathrm d y + (\cos y + y \cos x)\,\mathrm d x = 0 \\ \implies y\sin x + x\cos y = c$$

5. ## Re: integrating factor

Originally Posted by Archie
Perhaps the differentials are transposed. The following is exact:
$$(\sin x - x\sin y) \,\mathrm d y + (\cos y + y \cos x)\,\mathrm d x = 0 \\ \implies y\sin x + x\cos y = c$$
you mean the dy and dx should be interchanged , so that the equation is EXACT ?

6. ## Re: integrating factor

That's not a valid operation. I'm suggesting that the question has been written incorrectly.

7. ## Re: integrating factor

I will try and see

8. ## Re: integrating factor

Originally Posted by Archie
Perhaps the differentials are transposed. The following is exact:
$$(\sin x - x\sin y) \,\mathrm d y + (\cos y + y \cos x)\,\mathrm d x = 0 \\ \implies y\sin x + x\cos y = c$$
i tried this , but still didint get the answer . Is there any other alternative for this question?

9. ## Re: integrating factor

What answer are you looking for?

10. ## Re: integrating factor

Originally Posted by Archie
What answer are you looking for?
the ans given is xcosy + ycosx = C

11. ## Re: integrating factor

So the exact equation would be
$\displaystyle (\cos y - y\sin x) \, \mathrm d x + ( \cos x -x \sin y )\, \mathrm d y = 0$

12. ## Re: integrating factor

Originally Posted by Archie
So the exact equation would be
$\displaystyle (\cos y - y\sin x) \, \mathrm d x + ( \cos x -x \sin y )\, \mathrm d y = 0$
sorry , i made a mistake here , the ans given is xcosy + ysinx = C , so what should the question look like ?

See post #4.