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Asked Oct 17, 2019
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In Exercises 1-14 find a particular solution.
у" — 2у — Зу — е*(-8 + 3х)
3.
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In Exercises 1-14 find a particular solution. у" — 2у — Зу — е*(-8 + 3х) 3.

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Expert Answer

Step 1

We need to find  the particular solution only :

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1 1 - V f(D+a) We know (De)e where V is a function of x Here, we have y" - 2y-3y e(-8+3x) or.(D -2D-3) y =e" (-8 +3x) 1 (-8+3x)) or,y (D2-2D-3)

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Step 2

Now, let us apply the formula :

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Applying the formula: 1 1 (-8+3x) (D+1)-2(D+1)-3 (D2 2D-3) 1 (-8+3x D2-4 =e 1 (-8+3x (D-2) (D+ 2) (-8+3x) (D-2) (D+2)

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Step 3

Further, expanding the i...

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(-8+3x) (-8+3x) 2 2 e (-8+3x)+ (-8+3x) 1+ 2 2 (-8+3x)0 (-8+3x)+ 0.. 2 -e -16 6x Зе\x = 2e* 4

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