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2 answers:
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Note that if 
, then 
, and so we can collapse the system of ODEs into a linear ODE:
which is a pretty standard linear ODE with constant coefficients. We have characteristic equation
so that the characteristic solution is
Now let's suppose the particular solution is
. Then
and so
Thus the general solution for
is
and you can find the solution
by simply differentiating .
which is a pretty standard linear ODE with constant coefficients. We have characteristic equation
so that the characteristic solution is
Now let's suppose the particular solution is
and so
Thus the general solution for
and you can find the solution