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Asked Dec 14, 2019
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14. For what value of k, if any, will y= ke
+4 cos(3x) be a solution to the differential equation
y" + 9y = 26e-2 ?
of these materials online or in print
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14. For what value of k, if any, will y= ke +4 cos(3x) be a solution to the differential equation y" + 9y = 26e-2 ? of these materials online or in print

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The solutions to the differential equation are those that satisfies the e...

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-2x y" +9y= 26e -2x + 4 cos(3x) is a solution to the above differential equation. Hence, it will satisfy y = ke it. y' = -2ke* – 12sin (3x) y" = 4ke* – 36cos(3x) y" +9y = 26e2* 4ke* - 36 cos (3x) +9(ke* + 4cos(3.x))= 26e* -2x -2x 13ke 2x = 26e2x Compare both sides, we get 13k = 26 k = 2 Answer: The value of k is 2.

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