Question

solution of the given equations Find the general Y" - 3y = - 72 5ın 6oc - 72 cos loc + 3b es

Answer 1

62 solution: Given y"-364 = -72 sin 6x - 72 Cos 6x +36e" Let y = A (70) be a trial solution equation becomes Then the auxiliary m - 36=0 m=76 complementary function is i. The - 6x Where 4, Cz are arbitrary constant. To find particular integral we use method of undetermined coefficient. Now Yp is of the form Y p = Axe & Bsino at Closbx ... (2) = 6 Axeon & A G B Cosor a besin 6x 62 + GAe a 36 BSinox - 36 Ane 3) - 36C cos 6x ) we get in using (2), (3 ore Ge - 363 36B sinou 36 e Cos 62 36 Ane 46A e - 36 Axeon - 36 BSinga-36e cos 62 = – 72sinox - 72 Cos ou 43606x Op 12A 72 Bsingr - 72c cos 6x = -72sin 6x - 72 Cosor +36e comparing both side we get 12A = 36 or a=3 and - 72B = -72 CS Scanned with CamScadre, B=1 - 720=-72 or e=1

: y = 3x0+ sinore & Cosor Hence the general solution of the given differential equation is 64 y = qe tege 4 ne 4 sinte tlosbe CSScanned with CamScanner
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