## anonymous 5 years ago DE separation of variables: Is this right?

1. anonymous

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

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

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!

8. anonymous

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 :)

9. anonymous

ty

10. anonymous