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?