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

1. ## 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.

2. ## Re: Solve the equation y

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?

3. ## Re: Solve the equation y

I really dont know how to start it . it does not fit the methods I learn in the class.

4. ## Re: Solve y' = y-x-1+ 1/( x-y+2)

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.

5. ## Re: Solve y' = y-x-1+ 1/( x-y+2)

Try letting $y = x + u$.

6. ## Re: Solve y' = y-x-1+ 1/( x-y+2)

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...

7. ## 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.

8. ## 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.

9. ## Re: Solve y' = y-x-1+ 1/( x-y+2)

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,

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

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

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

I hope you can continue from here.