Question

Find a general solution of the ODE by using the method of undetermined coefficients.

24" - 5y + 2y = (t + 3)et/2

Answer 1

The desde of the green cam then 2 As e/2 is present on the role = 0, e2+ Gett. Zy - 56+ 2y = (t+13) e12 - 0 Amilliary equation is 2m² - 5 m +2 = 0 - Rom - 4m-m+2=0 => m=2, Complementary Juni the particular solution be 7 sa Atet/ ; Dys (A-A7%) e (1-7²2) Apr Dyp = A (1/2-1/4 - 4) = -2 2 2 A8% (@=> -20. % -5 (1-72) A eV2+2. Atete => ARY (- / +5 + +at) - 5 Aet = (x+3) et. Comparing the Coefficients 5 A eta Beta -> A=-3%. AOD 7000 pour de tet ..gp = - 13 The General Solution ac y ct y (t) = C, e 24 + 6, 83 83 tot