# integrating factor

#### Archie

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

#### xl5899

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

#### Archie

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

#### xl5899

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 ?

#### Archie

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

• 1 person

#### xl5899

I will try and see

#### xl5899

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?

#### Archie

What answer are you looking for?

#### xl5899

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