Why Is My Integrating Factor Not Solving the Exact ODE?

[ozone]

I'm not sure where I'm going wrong on this one so I hoped that I could find some help

we begin with
$(x^2 + y^2 + 5) dx - (y+xy) dy$

taking both partial derivitives I found that

$2y (dy) =/ -y(dx)$

Next I went to find my factor of integration using $e^(My - Nx / N) dx)$This got me $((1+x)^-3)$

which i then simplified to $(1 + 1/x^3)$Then i multiplied our I.F. through the original M and N, but the problem still did not come out to be equal

our new partial derivitives of m and n are:

$((2y/x^3)(dy) =/ ((3y/x^4) + (2y/x^3) - (y))(dx))$Sorry I couldn't figure out how to display notequal with itex.. anyways thanks in advance for any help

 

[HallsofIvy]

I'm not sure where I'm going wrong on this one so I hoped that I could find some help

we begin with
$(x^2 + y^2 + 5) dx - (y+xy) dy$

taking both partial derivitives I found that

$2y (dy) =/ -y(dx)$

Next I went to find my factor of integration using $e^(My - Nx / N) dx)$


This got me $((1+x)^-3)$

which i then simplified to $(1 + 1/x^3)$

Well, that's a problem! $(1+x)^{-3}$ is NOT equal to
$$1+ \frac{1}{x^3}$$
It is, rather,
$$\frac{1}{(1+ x)^3}$$

Then i multiplied our I.F. through the original M and N, but the problem still did not come out to be equal

our new partial derivitives of m and n are:

$((2y/x^3)(dy) =/ ((3y/x^4) + (2y/x^3) - (y))(dx))$


Sorry I couldn't figure out how to display notequal with itex.. anyways thanks in advance for any help

 

[ozone]

Sooo wolfram's mistaken??

http://www.wolframalpha.com/input/?i=distribute+(1+x)^-3

 

[HallsofIvy]

What do you think "distribute" means there?