Question

DE separation of variables: Is this right?

Answer 1

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

Answer 2

Integrating mistake; I think I drop the 1/2 so that it's just ln(9)=c...

Answer 3

Yeah, I got the same answer. Are you asked to solve y?!

Answer 4

Just solve initial condition of y(0)=2. Thanks!

Answer 5

Yeah I can see that. It's usually better to write the solution as a function of t, if possible.

Answer 6

hey anwar im srry to bother u but do you think you can help me after your donehere

Answer 7

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!

Answer 8

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 :)

Answer 9

ty

Answer 10

I can't find your problem!

Answer 11

ill repost it