Thread: separable differential equation

I can't seem to get the solution in my text book, the problem is:



I began by reorganizing to:



expanding the y term and integrating:



giving the following:



where K is the combined constant of integration from both sides
now when I take the exponential, I think I have to raise e to the entire
right side and that I can't do it term by term which simplifies to a division
using log properties and then canceling out the e and ln



now I was thinking I could drop all the absolute values if I throw a +\-
in front of the remaining exponential, so we'll say



solving for y yields:



however my textbook gives:



Please let me know if you can see my mistake, thanks

Originally Posted by stevedave

I can't seem to get the solution in my text book, the problem is:



I began by reorganizing to:



expanding the y term and integrating:



Wrong sign! Left side should be

..

Originally Posted by stevedave

I can't seem to get the solution in my text book, the problem is:



I began by reorganizing to:



expanding the y term and integrating:

. You have the sign wrong. You should have

giving the following:



where K is the combined constant of integration from both sides
now when I take the exponential, I think I have to raise e to the entire
right side and that I can't do it term by term which simplifies to a division
using log properties and then canceling out the e and ln



now I was thinking I could drop all the absolute values if I throw a +\-
in front of the remaining exponential, so we'll say

The sign error I pointed out above means this should be so y-1= Cxy, Cxy- y= (Cx-1)y= -1. That gives what your textbook says.

solving for y yields:



however my textbook gives:



Please let me know if you can see my mistake, thanks

bah, I always do stuff like that . I'll rework it and see what happens. Thanks

correction ...