Finding an Integrating Factor for Solving Differential Equations

[Phatman]

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: e^{int(1/n(dm/dy-dndx)dx}

The Attempt at a Solution

u(x)=e^{int(1/(xy+1)(y(x+y)d/dy-(xy+1)d/dx)dx}
this reduces to
e^{int((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.

 

[HallsofIvy]

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: e^{int(1/n(dm/dy-dndx)dx}

The Attempt at a Solution

u(x)=e^{int(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
e^{int((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]

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:

The Attempt at a Solution

( Please excuse the u(x) remnants I'm leaning how to use the white boar editor.)[/B]

this reduces to ( Please excuse the u(x) reminets I'm leaning how to use the white boar editor.)

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

 

[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.