(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A problem in classical mechanics, dealing with an object in space collecting mass as it passes through a dust cloud has led me to the following nonlinear ODE. I'm quite sure it is the correct equation, my old man checked it out. But being the engineer he is, he would just go ahead and solve it numerically, so he didn't have any advice past this point .

[tex]A\rho(\dot{x})^{2}+m_{0}\ddot{x}+A\rho x \ddot{x}=0[/tex]

3. The attempt at a solution

So my idea was to assume [tex]\ddot{x}=constant[/tex] (which left me fewer things to worry about than a second order Taylor expansion). That seems like an ok approximation to me. But I'm still left with a term involving [tex](\dot{x})^{2}.[/tex] That still qualifies as nonlinear right? I rarely encounter nonlinear equations, I'm really out of my area of knowledge here! So even with my approximation I am left with an equation with a form I have never seen before.

[tex](\dot{x})^{2}+xa=\frac{m_{0}a}{A\rho}[/tex]

Any ideas? This is really quite baffling to me. I don't have slightest idea how to proceed. I don't think a simple integrating factor is gonna take care of this thing.

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# Homework Help: ODE - Trying to Linearize

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