MHB Inexact Differential Equation with 4 Degree

jeffer vitola
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hello ... I wanted to demonstrate the solution of a differential equation, and as I do not yet know the latex language, then I take pictures of the leaves with my solutions ... the user who wants to give more solutions is well received and is welcome ...
att
jefferson alexander vitola (Smile)
https://www.physicsforums.com/attachments/1063._xfImport
https://www.physicsforums.com/attachments/1064._xfImport
att
jefferson alexander vitola (Smile)

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Looks correct to me...but a question though to the forum ...in trying to solve for the particular solution, would it be ok setting ##y_p=c_5e^{-x}## rather than ##y_p=c_5e^{-x}+c_6xe^{-x}##? unless i am missing something here...
 
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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