Question

Find the general solution of  

Answer 1

"Given y"" + 4y' + 7y = 0 the auxillary equation is m^2 + 4m + 7 = 0 = > m^2 + 4m + 4 + 3 = 0 = > (m + 2)^2 + 3 = 0 = > (m + 2)^2 = -3 m + 2 = plusminus 3i = > m = -2 plusminus 3i So the general solution of the de is y(t) = c_1 e^-2t cos (3t) + c_2 e^-2t sin (3t)."