Diff Eq Problem. Need help!

  • Thread starter hitmeoff
  • Start date
  • #1
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Homework Statement


This is part of a solution to a E&M example from a book. I am in the middle of following the solution and I come across this system of diff eq's:


[itex]y''=\omega z'[/itex]
[itex]z''=\omega (\frac{E}{B}-y')[/itex]


Homework Equations


Solution according to author is:

[itex]y(t)=C_{1}\cos (\omega t)+C_{2}\sin (\omega t)+(\frac{E}{B})t+C_{3}[/itex]
[itex]z(t)=C_{2}\cos (\omega t)-C_{1}\sin (\omega t)+C_{4}[/itex]


The Attempt at a Solution


So the author just says that this is easily solvable by differentiating the first and using the second to eliminate z''. Now I tried that, but correct me if Im wrong, this works out to :

[itex]z''=\frac{y'''}{\omega}[/itex]
[itex]y'''+\omega^{2}y''-\omega^{2}\frac{E}{B}=0[/itex]

So now do I solve this diff eq, to get y(t) and then use substitution to solve for z(t)?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
Sure, that looks like the right strategy.
 

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