MTH 312 Midterm: Mid 1-F16-Sol
Document Summary
Oct 07, 2016: (4 points) use the method of undetermined coe cients to nd only the form of the particu- lar solution of y 6y + 9y = 6x2 + 2xe3x. Homogeneous sol. of y 6y + 9y = 0. Auxiliary equation; m2 6m + 9 = 0, Particular sol. for y 6y + 9y = g1(x) + g2(x) Particular sol. for g1(x) yp1 = ax2 + bx + c ; and for g2(x) yp2 = (dx3 + ex2)e3x. The form of the particular solution yp = ax2 + bx + c + (dx3 + ex2)e3x: (4 points) evaluate the inverse laplace l 1(cid:26) 2s + 3 s2 + 2s + 5(cid:27) 2(s + 1) (s + 1)2 + 4. L 1(cid:26) 2(s + 1) (s + 1)2 + 4. 1 (s + 1)2 + 4(cid:27) = 2e t cos(2t)+
