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Find a particular solution to the nonhomogeneous differential equation ?′′+4?′+5?=10?+?−? y ′ ′ + 4 y...

Find a particular solution to the nonhomogeneous differential equation ?′′+4?′+5?=10?+?−? y ′ ′ + 4 y ′ + 5 y = 10 x + e − x . ??= y p = help (formulas) Find the most general solution to the associated homogeneous differential equation. Use ?1 c 1 and ?2 c 2 in your answer to denote arbitrary constants, and enter them as c1 and c2. ?ℎ= y h = help (formulas) Find the most general solution to the original nonhomogeneous differential equation. Use ?1 c 1 and ?2 c 2 in your answer to denote arbitrary constants. ?=

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tuyt sy = loxtet 0 The auxilary equation is 22+ 40+5=0 +6+2)!= -1 ar=-ti i te=é dx (Cicosx+G sinx) @ Let p= Axt of cet ③from ③ particular solution is - p= 2x-88 tet Answer ③ 2 Solution of homogeneous equation is ha e BX ( 4 cos(x)+ G Sim (x)) An

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