Question

Solve the following second order initial value problem by the method of undetermined coefficients: y'-8y' +16 y = 2e", y(0)=1, y'(0)=0.

Answer 1

y" - syt164 = 2940 we just determine perticular soln by method of wash undetermined coefficient let, y= Axel y'= 2Axent 4A Xeon " = 206+ & Axen + SAX + 16Añean from, 2AQA" TIGAR (72416Axean - L6Axe _ 32 AM TIGAX 92 = 2042 J ZA 69 = 20 qa The 7 A -1. so, ye 20 e an is the particular integral for and Homogenous part of equation 0 6-80 +16) jao Characteristic equation m emt16 =0 =) (- 40 m-4.4 67 Y-geen terren So, yo creat la acea tare an is the solution of sequation

70- - 1 = 4 4-1 y (a) = 49000 + 4 nenor Gentzen +4 nrega 746) = 4e, tl2 3 4+4-0 6444 andyto=0) =) C2= -9 So, sole is y = et quetxean (Aus)