MHB Derivation of Equation (11) from R Boundary Condition

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http://www.vibsys.put.poznan.pl/journal/2010-24/noga-2.pdf

Equations (9) leads to (11).

How from R boundary condition do we end up with the equation in (11)?
 
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dwsmith said:
http://www.vibsys.put.poznan.pl/journal/2010-24/noga-2.pdf

Equations (9) leads to (11).

How from R boundary condition do we end up with the equation in (11)?

Ok so I figured out what they have done but what does this equation do for them?
 

Thread 'A question about variables of integration'

I have the equation ##F^x=m\frac {d}{dt}(\gamma v^x)##, where ##\gamma## is the Lorentz factor, and ##x## is a superscript, not an exponent. In my textbook the solution is given as ##\frac {F^x}{m}t=\frac {v^x}{\sqrt {1-v^{x^2}/c^2}}##. What bothers me is, when I separate the variables I get ##\frac {F^x}{m}dt=d(\gamma v^x)##. Can I simply consider ##d(\gamma v^x)## the variable of integration without any further considerations? Can I simply make the substitution ##\gamma v^x = u## and then...
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