Question

Find a particular solution to the differential equation using the Method of Undetermined Coefficients. y" - y' + 196y = 14 sin (14) A solution is yp(t) =

Answer 1

ul 1 to y" -y + 196y = 14 sim (144) We will deformine the particular solution by the method of undetermined coefficients. Let the particular solution y"-y + 196y="14 ain (146) be Up? = Acos (14+) + B sin (147) y=-14A sin(14x) +143 cos(14+) and yi = -196 Acos(144)–196B AIN(1449 Substituting these values into the differential equation we get up -yp tiqbyp=14 sin (14+) 196 Acos (14+) -196 Bein (148) +14 Asin (14+)-14B cos (14+) + 196 Acos(146) 41968in (146) = 14 rin (kk) +-14B cos (144) +14A sin (144) = 14 sin (147) ..-14B=0>B=0 and 14A=14 > A=1 Hence a solution is yp(x) = cos(14+). -