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Math Help - solve second order eqn

  1. #1
    Junior Member ceode's Avatar
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    solve second order eqn

    D^2 (x) - 3 dx/dt + 2x = 0

    D^2 represents second order differential ie d/dt * d/dt

    Given that when t=0 , x=0 , dx/dt = 0
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  2. #2
    A Plied Mathematician
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    What ideas have you had so far?
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  3. #3
    Junior Member ceode's Avatar
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    Can i do it by this method

    Auxiliary equation is given by m^2 - m + 2 = 0
    we will get imaginary and distinct value for m...

    LiKE THAT
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  4. #4
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    Right in general. However, from your DE, you should have m^2 - 3m + 2 = 0. This is all within the framework of assuming a solution of the form x = A e^(m t), right?
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  5. #5
    Junior Member ceode's Avatar
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    Iam sorry , i make stupid mistakes. Now you know

    I got the C.F as

    x = c1 e^2t + c2 e^t

    Now what ?
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  6. #6
    Junior Member ceode's Avatar
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    i got m as 1 and 2 , which are distinct and real
    so by the formula given by our teacher i got the the above result
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  7. #7
    A Plied Mathematician
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    Excellent. All you have to do now is find out what the constants c1 and c2 are. You do that by plugging in the initial conditions. You're probably going to get a system of equations. What do you get?
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  8. #8
    Junior Member ceode's Avatar
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    c1 + c2 = 0
    c1 = - c2
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  9. #9
    A Plied Mathematician
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    There's one equation. You've applied the x(0) = 0 condition. But you also have the other condition: x'(0) = 0. What does that give you?
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  10. #10
    Junior Member ceode's Avatar
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    whats the other condition ?
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  11. #11
    A Plied Mathematician
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    Well, you've got the function x(t). What is x'(t)?
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  12. #12
    Junior Member ceode's Avatar
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    dx/dt = c1 2.e^2t + c2 . e^t
    0 = 2 c1 + c2
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  13. #13
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    Excellent. So, solving those two equations simultaneously should give you c1 and c2. What do you get?
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  14. #14
    Junior Member ceode's Avatar
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    i got c1 as 0 which means c2 also 0
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  15. #15
    Junior Member ceode's Avatar
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    Thank you very much for all your help......
    I dont hate the subject after all..
    I going to the hostel tomorow..... I dont like it there. The food is terrible
    Good bye
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