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 $$\ln(R^{n-1}) + mR^{n-1} = A$$ 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.