# Differential Equation problem

1. Sep 5, 2015

### MidgetDwarf

Solve the given differential equation by separation of variables.

(dy/dx)= (xy+3x-y-3)/(xy-2x+4y-8)

First, I noticed when i divided both sides by the left hand side and multiplied both sides by dx, nothing cancelled or seemed to work.

I got to thinking.

on the right hand side I preformed long division.

i divided xy+3x-y-3 by xy-2x+4y-8.

I get 1 + (5x-5y+5)/(xy-2x+4y-8)

(dy/dx)= 1 + (5x-5y+5)/(xy-2x+4y-8)

I am stuck here. Any help is welcomed and appreciated.

2. Sep 5, 2015

### Tallus Bryne

I think a better approach is beginning instead by factoring the RHS. From there it should be clear how to solve via separation of variables.

3. Sep 5, 2015

### MidgetDwarf

wow, i over thought this problem. thanks a lot.

factoring the left hand side.

(y+3)(x-1)/(y-2)(x+4)

Left hand side= (y-2)/(y+3)dy

right hand side=(x-1)/(x+4)dx

then I integrate. the process is kind of lengthy, requiring trivial integration.

I can't take you enough.

4. Sep 7, 2015

### Tallus Bryne

That looks like a correct implicit soln; you can also tidy up the RHS of your answer a little by applying some rules of exponents:
$$e^{x}e^{-y} = e^{x-y}$$

5. Sep 7, 2015

### MidgetDwarf

yes, you are correct. thanks a lot.

Do you recommended a an intro ode book?

we are using zill in our class, and it is a bit to chatty. The graphics make the layout of the book a little hard to read in my opinion and he is too loose ( doesn't really use mathematical language) in his explanations.

6. Sep 7, 2015

### Tallus Bryne

I wouldn't be able to help you there. I also used a text co-authored by Zill when I took differential ('Differential Equations with Boundary-Value Problems' by Zill and Cullen 7ed.) when I took differential.
I saw a text by Ross recommended in the thread "How to self-study mathematics?" However, I haven't ever had the opportunity to see what it's like myself.