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What kind of differential equation is this

  1. Nov 1, 2011 #1
    I am trying to solve a real-world problem, and I have modeled it with the following equation:
    [tex]\frac{dS}{dt}-3\left (\frac{150-S}{100-t} \right )+\frac{2S}{100+t}=0[/tex]

    What kind of differential equation is that? Is it solvable analytically ?
    Maple tells me it is linear, but I don't see how...
     
    Last edited: Nov 1, 2011
  2. jcsd
  3. Nov 1, 2011 #2

    lurflurf

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    I forget what that is called, but it is linear and easily solved. Clear denominators
    (t-100)(t+100)s'(t) = (t+500) s(t)-450 t-45000
    solve
    (t-100)(t+100) s'(t) = (t+500) s(t)
    use that to solve the original
    naturally terms like
    (t-100)m(t+100)n
    arise
     
    Last edited: Nov 1, 2011
  4. Nov 2, 2011 #3
    It is a first order linear ODE
    Of course it is easy to solve it, thanks to classical method.
    "Linear" means linear relatively to the sought function S (There is no S² nor other functions of S. There are only S and S' in the equation).
    It doesn't mean linear relatively to the variable t.
     
    Last edited: Nov 2, 2011
  5. Nov 2, 2011 #4
    Write: dS/dt + f(t)S = g(t).
     
  6. Nov 5, 2011 #5
    Looks like rate of equation that determines solution or volume of liquid into a tank and out. Again it is solvable via separable equations.
     
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