Equation of motion in tensorial form (relativistic)

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Homework Statement


How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge e and mass m, with 4-momentum p^a and electromagnetic field tensor F_{ab} of a constant magetic field \vec B perpendicular to the plane of motion. \frac{dp^a}{d\tau}=\frac{e}{m}F^a{}_bp^b
?
Let the the initial condition be p^a=(E_0 ,\vec 0)



Homework Equations


\frac{dp^a}{d\tau}=\frac{e}{m}F^a{}_bp^b


The Attempt at a Solution


I can see that the differential equation resembles that of a SHM equation or a cosh, sinh one if it's a scalar equation. However, I don't know how to deal with a tensor equation. Could anyone please explain? Thank you.
 
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This is a set of 4 simultaneous linear first order ordinary differential equations in 4 unknowns. Do you know how to solve such a set of equations?
 

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