# Solve y' = y-x-1+ 1/( x-y+2)

• Jul 7th 2011, 12:24 PM
ryan1573
Solve y' = y-x-1+ 1/( x-y+2)
Solve the ODE y' = y-x-1+ 1/( x-y+2) and give the solution in implicit form.
• Jul 7th 2011, 12:46 PM
Also sprach Zarathustra
Re: Solve the equation y
Quote:

Originally Posted by ryan1573
Solve the ODE y' = y-x-1+ 1/( x-y+2) and give the solution in implicit form.

Can we see some of your work on this problem?
• Jul 7th 2011, 03:48 PM
ryan1573
Re: Solve the equation y
I really dont know how to start it . it does not fit the methods I learn in the class.
• Jul 7th 2011, 07:15 PM
mr fantastic
Re: Solve y' = y-x-1+ 1/( x-y+2)
Quote:

Originally Posted by ryan1573
Solve the ODE y' = y-x-1+ 1/( x-y+2) and give the solution in implicit form.

Is it y' = y-x-1+ 1/( x-y+2) or y' = (y-x-1+ 1)/( x-y+2)? Big difference.
• Jul 8th 2011, 04:37 AM
Jester
Re: Solve y' = y-x-1+ 1/( x-y+2)
Try letting $\displaystyle y = x + u$.
• Jul 8th 2011, 04:39 AM
Prove It
Re: Solve y' = y-x-1+ 1/( x-y+2)
Quote:

Originally Posted by mr fantastic
Is it y' = y-x-1+ 1/( x-y+2) or y' = (y-x-1+ 1)/( x-y+2)? Big difference.

I doubt it would be the second, as there is no point in writing -1 + 1 in the numerator...
• Jul 8th 2011, 05:04 AM
ryan1573
Re: Solve y' = y-x-1+ 1/( x-y+2)
dy/dx = (y-x-1)+ 1/(x-y+2) is the correct equation. it is the first one.
• Jul 8th 2011, 05:24 AM
ryan1573
Re: Solve y' = y-x-1+ 1/( x-y+2)
I try y= x+u, dy/dx= 1+ （du/dx） dy/dx = (u-2)-[1/ (u-2)]. integrating u', I have u= 0.5 u^(2) - 2u- ln(u-2). I dont know how to do next.
• Jul 8th 2011, 06:55 AM
Sudharaka
Re: Solve y' = y-x-1+ 1/( x-y+2)
Quote:

Originally Posted by ryan1573
I try y= x+u, dy/dx= 1+ （du/dx） dy/dx = (u-2)-[1/ (u-2)]. integrating u', I have u= 0.5 u^(2) - 2u- ln(u-2). I dont know how to do next.

Hi ryan1573,

You have substituted incorrectly. It should be,

$\displaystyle 1+\frac{du}{dx}=u-1-\frac{1}{u-2}$

$\displaystyle \Rightarrow \frac{du}{dx}=(u-2)-\frac{1}{u-2}$

$\displaystyle \Rightarrow \frac{du}{dx}=\frac{(u-1)(u-3)}{u-2}$

I hope you can continue from here.