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## Main Question or Discussion Point

I was wonder if anybody might know how to solve this (this is not a homework problem, btw).

The Lorentz Force is given by:

[tex]\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})[/tex]

Now afer working that out, I get three differential equations:

[tex]\frac{dv_x}{dt}=\frac{q}{m}(E_x+v_yB_z-v_zB_y)[/tex]

[tex]\frac{dv_y}{dt}=\frac{q}{m}(E_y+v_zB_x-v_xB_z)[/tex]

[tex]\frac{dv_z}{dt}=\frac{q}{m}(E_z+v_xB_y-v_yB_x)[/tex]

So far so good. But I can't solve these differential equations because we have [tex]\frac{dv_x}{dt}[/tex] as a function of [tex]v_y[/tex] and [tex]v_z[/tex]

I would be thankful if anyone would show me how to solve such a system of differential equations.

The Lorentz Force is given by:

[tex]\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})[/tex]

Now afer working that out, I get three differential equations:

[tex]\frac{dv_x}{dt}=\frac{q}{m}(E_x+v_yB_z-v_zB_y)[/tex]

[tex]\frac{dv_y}{dt}=\frac{q}{m}(E_y+v_zB_x-v_xB_z)[/tex]

[tex]\frac{dv_z}{dt}=\frac{q}{m}(E_z+v_xB_y-v_yB_x)[/tex]

So far so good. But I can't solve these differential equations because we have [tex]\frac{dv_x}{dt}[/tex] as a function of [tex]v_y[/tex] and [tex]v_z[/tex]

I would be thankful if anyone would show me how to solve such a system of differential equations.