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Laplace Transform question

  1. Jul 27, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve df/dx (x)+ f(x)= 3 under the condition f(0)= -2 using the Laplace transformations

    2. Relevant equations


    3. The attempt at a solution
    Not even sure where to start on this one. Dont have any examples that point me in the right direction. Any ideas anyone??
     
  2. jcsd
  3. Jul 27, 2010 #2
    Do you know what is Laplace transform of f'(x) (for general f)? That's what makes Laplace transform a tool suitable to solving differential equation.
     
  4. Jul 27, 2010 #3
  5. Aug 13, 2010 #4
    Manged to final get to this answer:

    df/dx (x)+ f(x)= 3
    ℓ ( df/dx+ dx) = l 3
    ℓ ( df/dx )+ l (dx) = l 3
    ℓ ( df/dx )= f^' (x)= sF(s)- f(0)
    ℓ (dx) = F(s)
    ∴ sF(s)- f(0) + F(s) = l 3
    ∴ sF(s) – f(0) + F(s) = 3/s
    F(s)(s + 1) – f(0) = 3/s
    F(s)(s + 1) – (-2) = 3/s
    F(s)(s + 1) +2 = 3/s
    F(s)(s + 1) = 3/s – 2
    F(s) = 3/(s(s+1)) - 2/(s+1)
    3/(s(s+1)) = 3/s- 3/(s+1)
    ∴ F(s) = 3/s - 3/(s+1) - 2/(s+1)
    ∴ F(s) = 3/s - 5/(s+1)
    l^(-1) (3/s ) = 3
    l^(-1) (5/(s+1) )= 〖5e〗^(-t)

    ∴ F(s) = 3 - 5e^(-t)


    think its pretty good but would like some feedback. Cheers.
     
  6. Aug 13, 2010 #5

    vela

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    Looks good though there are some typos. The last line should be f(t)=..., not F(s)=....
     
  7. Aug 16, 2010 #6
    Thanks Vela. If thats all i got wrong then i am quite happy!
     
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