Special Integrating Factors

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



Homework Equations


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

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.
 

Answers and Replies

  • #2
HallsofIvy
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1. solve the problem first finding an integrating factor of susceptible form.
y(x+y)dx+(xy+1)dy=0



Homework Equations


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

The Attempt at a Solution


u(x)=eint(1/(xy+1)(y(x+y)d/dy-(xy+1)d/dx)dx
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!

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.
 
  • #3
3
0
1. solve the problem first finding an integrating factor of susceptible form.
y(x+y)dx+(xy+1)dy=0



Homework Equations


form: M(x,y)dx+N(x,y)dy=0
intigrating factor:
inigrating factor.jpg


The Attempt at a Solution

( Please excuse the u(x) remnants i'm leaning how to use the white boar editor.)[/B]
inigrating factor#2.jpg

this reduces to ( Please excuse the u(x) reminets i'm leaning how to use the white boar editor.)
inigrating factor#3.jpg


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.
edited to make it easier to read
 
  • #4
3
0
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.
 

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