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shards5

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## Homework Statement

y"' - 9y" +18y' = 30e

^{x}

y(0) = 16

y'(0) = 14

y"(0) = 11

## Homework Equations

n/a

## The Attempt at a Solution

Factor Out

r(r

^{2}- 9r +18)

r = 0; r = 6; r =3

General Equation

y(x) = c

_{0}+ c

_{1}e

^{3x}+ c

_{2}e

^{6x}

y'(x) = 3c

_{1}e

^{3x}+ 6c

_{2}e

^{6x}

y"(x) = 9c

_{1}e

^{3x}+ 36c

_{2}e

^{6x}

c

_{1}= (11 - 36c

_{2})/9

y'(x) = 14 = 3c

_{1}e

^{3x}+ 6c

_{2}e

^{6x}

y'(x) = 14 = ((11 - 36c

_{2})/9)e

^{3x}+ 6c

_{2}e

^{6x}

c

_{2}= -31/30

c

_{1}= (11 - 36*(-31/30))/9 = 5.35555556

y(0) = 16 = c

_{0}+ c

_{1}e

^{3x}+ c

_{2}e

^{6x}

16 +31/30 - 5.35555556 = c

_{0}= 11.6777778

Solve For A in Ae

^{x}

y

_{p}= Ae

^{x}

y'

_{p}= Ae

^{x}

y"

_{p}= Ae

^{x}

y"'

_{p}= Ae

^{x}

Inputting into the original equation we get.

Ae

^{x}- 9Ae

^{x}+18Ae

^{x}= 30e

^{x}

Simplifying we get.

10Ae

^{x}= 30e

^{x}

Which gives A = 3 and since 3 is a root of the original equation we add an x to differentiate between the two.

So the final equation SHOULD BE 3xe

^{x}+ 11.6777778 + 5.35555556e

^{3x}-31/30e

^{6x}but of course its not.

So my question is, what am I doing wrong?

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