ELEC1704 Further Engineering Mathematics Problem sheet - Week 20 1. Find the solution for the following coupled systems of LDEs (a) yi + y1 + 6y2 = o o 2y2 + 2y1 + 4y2 = ( b ) y1 + 3y1 + 6y2 = y2 + y1 + 2y2 = 2. Find the particular solution for the following systems of LDEs: (a) yi + y1 + 6y2 = 5x 2y2 + 2y1 + 42 = x 2 (b) yity1 + 6y2 = 2y'2 + 2y1 + 4y2 = cos(x) (c) yi + 3y1+ 6y2 = 2 12 + y1 + 2y2 0 3. Given the following 2"d order LDE: 2y" + 5y -3y=0 with y(0) = -4 and y'(0) =9 (a) Convert this LDE into a system of coupled 1s order LDEs. (b) Solve the system of coupled 1st order LDEs of part (a). (c) Solve the 2"d order LDE using the method discussed earlier, and show that the two solutions are identical. 4. Given the following 3'd order LDE: y" + 3y"+ 3y'ty=0 with y(0) =7, y'(0) =-7 and y"(0) =11 (a) Convert this LDE into a system of coupled 1st order LDEs. (b) Solve the system of coupled 15 order LDEs of part (a). 5. Given the following 2nd order LDE: y " - 2y' ty = ex with y(0) = 1 and y'(0) =2 (a) Convert this LDE into a system of coupled 15 order LDEs. (b) Find the complementary solution for the coupled 15 order LDEs. (c) Find the particular solution for the coupled 15 order LDEs. (d) Find the specific solution of the LDE