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anonymous

  • 5 years ago

DE separation of variables: Is this right?

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  1. anonymous
    • 5 years ago
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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

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

  3. anonymous
    • 5 years ago
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    Yeah, I got the same answer. Are you asked to solve y?!

  4. anonymous
    • 5 years ago
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    Just solve initial condition of y(0)=2. Thanks!

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

  6. anonymous
    • 5 years ago
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    hey anwar im srry to bother u but do you think you can help me after your donehere

  7. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    ty

  10. anonymous
    • 5 years ago
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    I can't find your problem!

  11. anonymous
    • 5 years ago
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    ill repost it

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