How do I solve this differential equation:

$\displaystyle m\frac{d^2x(t)}{dt^2}=\frac{-c}{x(t)^2}$, c and m are constants larger than 0. Initial conditions are x(0)=a, x'(0)=0.

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- Feb 15th 2007, 01:15 PMEne Denedifferential equation
How do I solve this differential equation:

$\displaystyle m\frac{d^2x(t)}{dt^2}=\frac{-c}{x(t)^2}$, c and m are constants larger than 0. Initial conditions are x(0)=a, x'(0)=0. - Feb 15th 2007, 01:18 PMEne Dene
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 - Feb 15th 2007, 01:53 PMtopsquark
FYI LaTeX is down at the moment. Please stay tuned for futher details. News at 11. :)

-Dan - Feb 15th 2007, 07:34 PMThePerfectHacker
- Feb 16th 2007, 02:27 AMEne Dene
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. - Feb 16th 2007, 05:47 AMtopsquark
- Feb 16th 2007, 06:55 AMThePerfectHacker
- Feb 16th 2007, 09:39 AMEne Dene
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 - Feb 16th 2007, 01:23 PMtopsquark
- Feb 16th 2007, 01:35 PMEne DeneQuote:

Originally Posted by**topsquark**

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