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I know I should use \(F(x)=m\ddot x\) somwhere...

somewhere*

The \(e^{stuff}\) will probably come from integration with \(x\)'s in the denominator.

That might do it, thanks!

I'll look into it..

I'll start by integrating with respect to \(t\) :)

Or not.. I'll see...

Thanks! :)

When I said trig substitution I mean hyperbolic trig function btw haha.

They should be the same, I think.

I suppose I'm really taking the long way, sorry! Haha. Yes, they're the same though.

You can alternatively use
\(x(t)=C\cosh (\alpha x) + D \sinh (\alpha x)\)

I'd really rather not use the hyperbolic trigonometric functions, haha!!

If initial velocity is zero, then the hyperbolic functions are simpler.

Sorry, I meant :
\(x(t)=C\cosh (\alpha t) + D \sinh (\alpha t)\)

Ohhh, okay! Thanks! :)

And I got it with the initial conditions :) Thank you both! :)