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Math Help - differential equation

  1. #1
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    Question differential equation

    How do I solve this differential equation:
    m\frac{d^2x(t)}{dt^2}=\frac{-c}{x(t)^2}, c and m are constants larger than 0. Initial conditions are x(0)=a, x'(0)=0.
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  2. #2
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    I don't understand what did I do wrong with latex syntax.

    If someone doesn't understand what I wrote:
    m*x''(t)=-c/x(t)^2
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  3. #3
    Forum Admin topsquark's Avatar
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    FYI LaTeX is down at the moment. Please stay tuned for futher details. News at 11.

    -Dan
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  4. #4
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    Quote Originally Posted by Ene Dene View Post
    How do I solve this differential equation:
    m\frac{d^2x(t)}{dt^2}=\frac{-c}{x(t)^2}, c and m are constants larger than 0. Initial conditions are x(0)=a, x'(0)=0.
    Solve initial value problem from the general solution.
    Attached Thumbnails Attached Thumbnails differential equation-picture18.gif  
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  5. #5
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    I don't understand something, if you have a harmonic oscilator differential equation:
    x''(t)+a^2*x(t)=0,
    the solution is:
    x(t)=Acos(a*t)+Bsin(a*t).

    So why don't you get solution x(t)? Or do you suggest that solution is:
    x(t)=c1+c2*t+c/m*ln(t) ?
    If so, I don't think that's a solution, try puting it in initial equation.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Ene Dene View Post
    I don't understand something, if you have a harmonic oscilator differential equation:
    x''(t)+a^2*x(t)=0,
    the solution is:
    x(t)=Acos(a*t)+Bsin(a*t).

    So why don't you get solution x(t)? Or do you suggest that solution is:
    x(t)=c1+c2*t+c/m*ln(t) ?
    If so, I don't think that's a solution, try puting it in initial equation.
    Well, if c = 0 it works. Then the solution is x(t) = c1 + c2*t

    -Dan
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  7. #7
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    Quote Originally Posted by Ene Dene View Post
    I don't understand something, if you have a harmonic oscilator differential equation:
    x''(t)+a^2*x(t)=0,
    the solution is:
    x(t)=Acos(a*t)+Bsin(a*t).

    So why don't you get solution x(t)? Or do you suggest that solution is:
    x(t)=c1+c2*t+c/m*ln(t) ?
    If so, I don't think that's a solution, try puting it in initial equation.
    No sure what you are asking.

    You asked to solve,
    x^2x''=.....

    But you wrote,
    x''+a^2x=.....

    They are different equations.

    I solved the upper one, and I think that is the one you wanted to be solved.
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  8. #8
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    I can't understand how is x(t)=C1+C2*t+c/m*ln(t) solution of equation x''(t)+c/(m*(x(t))^2)=0.

    x''(t)=-(c/m)/t^2.

    And then we have:

    -(c/m)/t^2+c/(m*(C1+C2*t+c/m*ln(t))^2)=!0
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  9. #9
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Ene Dene View Post
    I can't understand how is x(t)=C1+C2*t+c/m*ln(t) solution of equation x''(t)+c/(m*(x(t))^2)=0.

    x''(t)=-(c/m)/t^2.

    And then we have:

    -(c/m)/t^2+c/(m*(C1+C2*t+c/m*ln(t))^2)=!0
    Quote Originally Posted by topsquark View Post
    Well, if c = 0 it works. Then the solution is x(t) = c1 + c2*t

    -Dan
    Did you miss this post? You have a solution that works! (Whether or not the ln term is extraneous. I assume there's a reason it comes into the solution.)

    -Dan
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  10. #10
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    Quote Originally Posted by topsquark
    Did you miss this post? You have a solution that works! (Whether or not the ln term is extraneous. I assume there's a reason it comes into the solution.)
    In my first post I said that c>0. x(t)=c1+c2*t+c/m*ln(t) is just not a solution.

    Anyway it doesn't matter anymore, I've maneged to solve the problem by avoiding this differential equation (it was a physics problem).
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