Question about ExB position derivation

[johncoxon]

I have a question about the derivation on https://github.com/scipython/plasma-projects/blob/master/ExB/ExB%20drift%20for%20constant%20crossed%20electric%20and%20magnetic%20fields.ipynb. How do you get the forms of $$\dot{x}$$ and $$\dot{y}$$? I've been looking for a source that explicitly does the derivation, but I can't find one. I don't suppose you have a step-by-step version of the derivation? Thank you!

[xnx]

I think you just integrate $\ddot{x}$ to get $\dot{x}$ and substitute into the expression for $\ddot{y}$, don't you? You get something non-homogeneous: the complementary equation is simple harmonic and the particular integral a constant. Add them and apply the boundary conditions... I'll try to add the derivation when I get a moment.

[xnx]

I've added a derivation now, but I now think there might be a sign error in the expressions for $\dot(y)(t)$ and $y(t)$ used in the simulation. Perhaps you can confirm?