Special Integrating Factors

1. Apr 27, 2015

Phatman

1. solve the problem first finding an integrating factor of susceptible form.
y(x+y)dx+(xy+1)dy=0

2. Relevant equations
form: M(x,y)dx+N(x,y)dy=0
intigrating factor: eint(1/n(dm/dy-dndx)dx

3. The attempt at a solution
u(x)=eint(1/(xy+1)(y(x+y)d/dy-(xy+1)d/dx)dx
this reduces to
eint((x+y)/(xy+1))dx

This is where I need help. my integration is not good. I know that if I can solve for the integrating factor then I can solve for the equation because it will be in exact form.

Thanks for any help.

2. Apr 28, 2015

HallsofIvy

Staff Emeritus
This makes no sense to me. Your integrand is a function of x and y but you are integrating with respect to x so the exponent will be a function of y only yet you say that equals a function of x!

3. Apr 28, 2015

Phatman

edited to make it easier to read

4. Apr 28, 2015

Phatman

Halsofivy, you are right u(x) should be in terms of x. the way it works out in the book examples is y gets factored out while solving for the intigal. leaving only a function of x.