separation of variables

[Aerosion]

1. The problem statement, all variables and given/known data

so here's my equation:

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

so what i did first was factor out the right side

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

then i did a bunch of manipulation to get the ys on one side and the xs on another (i won't write this out right now but if anyone wants me to i can)

and got

(y-2)/(y+3) dy = (x-1)/(x+4) dx

of course i integrate, i get

y-5*ln(y+3) = x-5ln(x+4)

i want to get rid of the lns, right? so i multiplied them by e (like e^(ln(y+3)

then i got -4y-15=-4x-20

i'm not sure what to do after this because i looked at the answer at the back of my book and it said something completely different to what i've done so far, any help?



2. Relevant equations



3. The attempt at a solution

[gabbagabbahey]

Shouldn't your exponent for e be the entire expression on each side of the equation?

i.e.

e^{y-5ln(y+3)}=e^{x-5ln(x+4)}