# 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.