Finding an Integrating Factor for Solving Differential Equations

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.
 
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Phatman said:
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.
 
Phatman said:
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
 
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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