Re: [Phys-l] a nonlinear ODE

[jhowell@earlham.edu]

Hi Carl (et al.)

I don't have a solution to your problem, but I thought it might be useful
(though maybe discouraging) to point our that your solution for x(t) has
infinite acceleration at t = 0.  Does your solution need to be
well-behaved at t = 0?

John

> Consider the following differential equation for motion in a single
> variable x:
>
> x*a=k*t
>
> where x=position, a=acceleration, t=time, and k=real positive constant.
>
> What is the general solution for x(t)?
>
> By trying x=c*t^n, I get x=sqrt(4k/3)*t^1.5. But isn't that just a
> particular solution? Shouldn't I expect two arbitrary constants in the
> general solution?
>
> I'm somewhat unsure since I have little intuition about nonlinear
> equations. -Carl
>
> ---
> Carl E Mungan, Assoc Prof of Physics  410-293-6680 (O) -3729 (F)
> Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-5002
> mailto:mungan@usna.edu     http://usna.edu/Users/physics/mungan/
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