I need help filling in the blanks please. All the coefficients in the above ODEs

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I need help filling in the blanks please.

All the coefficients in the above ODEs are constants, In chapter 2 we would correctly assume a homogeneous solution beginning with y(t) = e lambda t, but assign constants to eventually develop the general solution to the homogeneous ODE. Here we do something similar. Here we assign subscripted constants at the beginning, to indicate which function, x,(t) or x,(t), they belong, i.e., And so Or, Substituting (5a b) into 4, and dividing through by e lambda t give

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