Please explain only the circled part in yellow. How did they come to this form of the method of undetermined coefficients. Which equation did they use.? According to me the x pi is wrong.

Example 1.16 Solve the system (D + 1) [x] - (D + 1) [y] = et (D - 1) [x] + (2D + 1) [y] = 5 2 by using the elimination method (operator method). Eliminate y first. Solution Eliminating y first we find: (2D + 1) [(1)] : (2D2 + 3D + 1) [x] - (2D2 + 3D + 1) [y] = (2D + 1) [et] = 3et (3) (D + 1) [(2)] : (D2 - 1) [x] + (2D2 + 3D + 1) [y] = (D + 1) [5] =5 (4) (3) + (4) : 3D (D + 1) [a] = 3et + 5. (5)From the auxiliary equation m (m + 1) = 0 we have m = 0 or m = -1 so that the complementary function is given by XC.F. (t) = c1+ cze-t with ci and c2 arbitrary constants. We find the particular integral xp.I. (t) by using the method of un termined coefficients: Let XP.I. (t) = Aet + Bt so that acp.I. (t) = Aet + B 3CP.I. (t) = Aet.Substituting these equations in (5) we find 6Act + 3B = 3et + 5. Comparing coefficients we find A = NIH and B = so that XP.I. (t ) = e t