DE separation of variables: Is this right?

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DE separation of variables: Is this right?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Solve the following problem using separation of variables. \[dy/dt = (y ^{2}+5)/2y\] \[2y * dy/dt=y ^{2}+5\] \[\int\limits2y/(y ^{2}+5)dy=\int\limits dt\] \[u=y ^{2}+5\] \[du=2ydy\] \[1/2\int\limits 1/u du = 1/2 \ln(y ^{2}+5)\] \[1/2 \ln(y ^{2}+5)=t+c\] At y(0)=2: \[1/2 \ln(2^{2}+5)=0+c\] 1/2 ln (9)=c
Integrating mistake; I think I drop the 1/2 so that it's just ln(9)=c...
Yeah, I got the same answer. Are you asked to solve y?!

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Just solve initial condition of y(0)=2. Thanks!
Yeah I can see that. It's usually better to write the solution as a function of t, if possible.
hey anwar im srry to bother u but do you think you can help me after your donehere
We didn't have to do that for this problem. I'm reviewing for a cumulative final on Wednesday; these questions are from early in the semester!
I see. Good luck. @nath: I'll have a look at your problem. But to let you know, I am not good at series in general :)
ty
I can't find your problem!
ill repost it

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