Differential Equation from a Physics Problem

In order to solve a problem I need to solve the following differential equation:

http://latex.codecogs.com/gif.latex?...2}}+v^2x^{{x}}

I'll figure out how to do any integration or differentiation that's necessary, but I don't know how to get it into a form that I can work with. If anyone could please show me how to get to a point from which I can integrate or differentiate?

Re: Differential Equation from a Physics Problem

Hi mate,

I think that this one needs integrating factors.

What I would do is divide everything by mv, and then take the (vx^x)/m term to the other side. This will give you the standard form of a non-separable first order ode (google this if you are unsure of the method). Your integrating factor is then e^(-int (x^x)/m) - but this is very hard to integrate. You could then rearrange and solve for v(x).

Re: Differential Equation from a Physics Problem

This is not going to be pretty...

This is a Bernoulli DE, so let

and substituting into the DE gives

which is first order linear, so multiplying by the Integrating Factor gives

Unfortunately, these integrals do not have closed-form solutions, so I don't know how much use they will be to you...

Re: Differential Equation from a Physics Problem

I don't need to integrate indefinitely, so I can use a Riemann sum or something. I don't know anything about integrating factors and different type of differential equations so I'm not surprised I couldn't do it. Thanks so much! You really are amazing 'Prove It'. =)

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Re: Differential Equation from a Physics Problem

Re: Differential Equation from a Physics Problem

It's recognising that you have a product rule expansion for a derivative in reverse - I also realise I've made a mistake in that step, as the integrating factor should actually have a negative in it. Doesn't change the result much though...