# a first order separable differential equations solution

#### kotongo

##### New member
Hi to all,

I have this beautifull diff. eq. : y'=(1-y^2)/(1-x^2)
the solution is not a problem. (also with Derive6 or Ti89) y=(c(x+1)+x-1)/(c(x+1)-x+1)
but the book says : y=(x+c)/(cx+1) and verifying is correct too.
axes traslstions ? or something else ?

Thanks.

#### Jomo

##### Elite Member
Hi to all,

I have this beautifull diff. eq. : y'=(1-y^2)/(1-x^2)
the solution is not a problem. (also with Derive6 or Ti89) y=(c(x+1)+x-1)/(c(x+1)-x+1)
but the book says : y=(x+c)/(cx+1) and verifying is correct too.
axes traslstions ? or something else ?

Thanks.
Combine constant. For example, c+1 simply becomes C.

#### Dr.Peterson

##### Elite Member
Hi to all,

I have this beautifull diff. eq. : y'=(1-y^2)/(1-x^2)
the solution is not a problem. (also with Derive6 or Ti89) y=(c(x+1)+x-1)/(c(x+1)-x+1)
but the book says : y=(x+c)/(cx+1) and verifying is correct too.
axes traslstions ? or something else ?

Thanks.
They are just using a different C, perhaps after simplifying. (They probably used a different method to get it.)

If we rewrite yours to make it look a little more like theirs, we get $$\displaystyle \frac{(c+1)x + (c-1)}{(c-1)x + (c+1)}$$.

Try dividing numerator and denominator by (c+1), and see if you can make it look just like theirs, once you define a new constant C.

#### kotongo

##### New member
Perfect Thanks a lot !

(%i1) solve((c*(x+1)+x-1)/(c*(x+1)-x+1)=(x+k)/(k*x+1),k);
c - 1
(%o1) [k = -----]
c + 1
Aslo with maxima online