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