a first order separable differential equations solution

kotongo

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Jan 4, 2019
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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 ? :confused:

Thanks.
 
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 ? :confused:

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

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.
 
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