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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 I am 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)?