Suppose that all the roots of the characteristic polynomial of a linear, homogeneous differential equation, with constant coefficients are, −2+3i,−2−3i,7i,7i,−7i,−7i,5,5,5,−3,0,0 (a) Give the order of the differential equation (b) Give a real, general solution of the homogeneous equation. (c) Suppose that the equation were non-homogeneous, and the forcing term, right-hand side of the equation, were t 2
e −2t
sin(3t). How does the general solution change? You only need to specify the part that does change. You do not need to write the entire general solution a second time.