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