Rearrange equation (solution of ODE)

[Juggler123]

I have determined the solution to a nonlinear first order ordinary differential equation but am struggling to rearrange the result, I have that

$$\\ln(R)+\frac{mR^{n-1}}{n-1}=\bar{w}_{\infty}\xi+C.$$

How would I rearrange this equation for $$R$$?

 

[Stephen Tashi]

Do you mean that R(x) is the function that solves a differential equation in the variable x ?

 

[pasmith]

I have determined the solution to a nonlinear first order ordinary differential equation but am struggling to rearrange the result, I have that

$$\\ln(R)+\frac{mR^{n-1}}{n-1}=\bar{w}_{\infty}\xi+C.$$

How would I rearrange this equation for $$R$$?

You can't. What you have is essentially <br /> \ln(R^{n-1}) + mR^{n-1} = A which doesn't have an analytic solution for R^{n-1} given A.

 

[Juggler123]

Sorry I should have been more clear. I have determined the solution R(\xi), the solution is

$$\ln(R(\xi))+\frac{mR(\xi)^{n-1}}{n-1}=\bar{w}_{\infty}\xi+C.$$

I simply need to rearrange this to say R(\xi)=\cdots

 

[HallsofIvy]

That was clear. And what you have been told that there is no solution in terms of elementary functions.

 

[Mark44]

The question has been asked and answered, so I'm closing this thread.