G(t) = ( 6e?t 0 ) = e?t ( 6 0 ) . Since the homogeneous
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G(t) = ( 6e?t 0 ) = e?t ( 6 0 ) . Since the homogeneous equation has a solution of the form xp(t) = e?t a, it is necessa
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G(t) = ( 6e?t 0 ) = e?t ( 6 0 ) . Since the homogeneous equation has a solution of the form xp(t) = e?t a, it is necessary to include both te?t a and e?t b in the assumed form for the particular solution, xp(t) = e?t b + te?t a. Substitute this expression into Eq. (ii) using the given g and show that a and b must be selected to satisfy (A + I2)a = 0, (A + I2)b = a ? ( 2 0 ) . Then find a and b that satisfy both of these equations.
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