# Need help with this differential equation using separation of variables.

## Homework Statement

The differential equation I have is dy/dx = (xy + 2y - x - 2)/(xy - 3y + x - 3). I need help getting started. Neither the top nor the bottom can be factored, so I don't know what to do next. Can anyone give me a push? All I know is that I need to use separation of variables.

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Redbelly98
Staff Emeritus
Homework Helper
Neither the top nor the bottom can be factored, so I don't know what to do next. Can anyone give me a push? All I know is that I need to use separation of variables.
The top and bottom can both be factored ... try again.

LCKurtz
Homework Helper
Gold Member

## Homework Statement

The differential equation I have is dy/dx = (xy + 2y - x - 2)/(xy - 3y + x - 3). I need help getting started. Neither the top nor the bottom can be factored, so I don't know what to do next. Can anyone give me a push? All I know is that I need to use separation of variables.
Hint: Your numerator can be factored:

(xy + 2y - x - 2) = y(x + 2) - (x + 2) = (x + 2)(y - 1).

Similarly in the denominator.

Oh, of course. Okay, so now I have (x+2)(y-1) on top, and (x-3)(y+1). I have separated those out. Now I have (y+1)/(y-1) dy = (x+2)/(x-3) dx. Is this the correct equation I need to solve?

Redbelly98
Staff Emeritus
Looking good so far 