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[Phys-l] a nonlinear ODE



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

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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/