Question

point) As an illustration of the difficulties that may arise in using the method of undetermined coefficients, consider 0 a. Form the complementary solution to the homogeneous equation. c(t)-c +, 02 ai -e®a, where a b. Show that seeking a particular solution of the form Walt s a constant vector does not work. In fact, if had this form, we would arrive at the following contradiction: d1 and a1- c. Show that seeking a particular solution of the form jp(t) te"a, where a-dii ls a constant vector,does not work either, In fact,i a2 Up had this form, we would arrive at the following contradiction: a2 a1 and al a2 is a constant vector, does not work. In fact, if İp had eta, where a b. Show that seeking a particular solution of the form yp t this form, we would arrive at the following contradiction: .7 αι and a1- c. Show that seeking a particular solution of the form p(t)te a, wereis a constant vector, does not work either. In fact, if Up had this form, we would arrive at the following contradiction: a1 and and

Answer 1

3 3-d det 아 什 6f

edr 64 3 6t 60, te 什+. test eç千 abin 6 test 3a 3a, 2 3 303010