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

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- Jul 7th 2011, 12:24 PMryan1573Solve 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 PMAlso sprach ZarathustraRe: Solve the equation y
- Jul 7th 2011, 03:48 PMryan1573Re: 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 PMmr fantasticRe: Solve y' = y-x-1+ 1/( x-y+2)
- Jul 8th 2011, 04:37 AMJesterRe: Solve y' = y-x-1+ 1/( x-y+2)
Try letting $\displaystyle y = x + u$.

- Jul 8th 2011, 04:39 AMProve ItRe: Solve y' = y-x-1+ 1/( x-y+2)
- Jul 8th 2011, 05:04 AMryan1573Re: 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 AMryan1573Re: 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 AMSudharakaRe: Solve y' = y-x-1+ 1/( x-y+2)
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.