Solve

I have tried finding a factor to make this equation exact, and I get . I then integrate by parts with respect to x and get

I feel like I'm not getting anywhere because nothing cancels like it should. Can someone please help me? Thanks!

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- February 9th 2011, 12:51 PMduaneg37making equation exact
Solve

I have tried finding a factor to make this equation exact, and I get . I then integrate by parts with respect to x and get

I feel like I'm not getting anywhere because nothing cancels like it should. Can someone please help me? Thanks! - February 9th 2011, 02:23 PMGeneral
Rewrite your differential as

Multiplying by the integrating factor

The last equation is exact. Its solution of the form where :

... (1)

... (2)

I think you integrate (1) with respect to x. This is too complicated .

Try to integrate (2) with respect to y and put p(x) as the constant of integration. - February 9th 2011, 05:47 PMduaneg37
Now I integrate w.r.t.y

Now I take partial w.r.t.x

I thought things would cancel if it was exact. Can anyone tell me what I'm doing wrong? Thanks! - February 9th 2011, 07:29 PMduaneg37

This is how I get

How do you get x+1? - February 9th 2011, 08:01 PMtopsquark
- February 9th 2011, 08:31 PMtopsquark
Okay, now that I've fixed my little problem with the minus signs...

(1) isn't difficult to integrate, but it is tedious. You should get

What I've always done from here is to integrate (2). This is an easy one. Then just match up common terms. It saves from having to work with the derivative of what you called p(x).

-Dan - February 9th 2011, 09:08 PMduaneg37

Does this look right? What technique did you use to integrate ? - February 9th 2011, 11:06 PMtopsquark

So we need to evaluate the integral

The second integral we can evaluate directly:

For the first integral use a = x + 1:

You can fill in the rest from there.

-Dan - February 9th 2011, 11:14 PMtopsquark
- February 10th 2011, 05:40 AMGeneral