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Homework Help: Separable Equation with Condition?

  1. Mar 31, 2008 #1
    [SOLVED] Separable Equation with Condition?

    1. The problem statement, all variables and given/known data
    Solve.
    http://www.mcp-server.com/~lush/shillmud/int3.71.JPG

    2. Relevant equations

    3. The attempt at a solution
    I'm not sure how to separate this. Also, since the directions consist of only one word, I'm not sure if y(2)=2 is some kind of hint or an additional condition to be fulfilled. I'm wondering where to go after factoring t out of the top. Thanks.
    http://www.mcp-server.com/~lush/shillmud/int3.72.JPG
     
  2. jcsd
  3. Mar 31, 2008 #2

    nicksauce

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    Science Advisor
    Homework Helper

    Well after factoring... you separate (hence separable equations!)

    [tex]\frac{dy}{y+3} = \frac{t}{t^2+1}dt[/tex]

    Then integrate both sides.
    y(2) = 2 is an initial condition, not a hint... After solving for y(t) you will have one arbitrary constant, which can be solved for using this condition.
     
  4. Mar 31, 2008 #3
    Wow, that seems almost too easy. Thanks.
     
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