MHB A NEW Method for solving differential equation - case studies

ysammour
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Hi,
This is a NEW method for solving differential equations - Case Studies. Please go to this website to see how:
http://www.sysins.com
Thanks.
Yousif Sammour.
 
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Frankly I don't see anything new here. It looks to me like a power series solution written in an unusually complicated way.
 
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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