Question
Asked Oct 17, 2019
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In Exercises 1-14 find a particular solution.
-3х (35 — 8х)
у" - бу' + 5у %3D е
2.
=
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In Exercises 1-14 find a particular solution. -3х (35 — 8х) у" - бу' + 5у %3D е 2. =

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Expert Answer

Step 1

The particular solution (P.S) of the given differential (D.E) equation find as follows,

d
Let D
dx
The D.E is written as,
(D2-6D+5) y e (35-8.x)
(D -6D+5)y 35e -8xe
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d Let D dx The D.E is written as, (D2-6D+5) y e (35-8.x) (D -6D+5)y 35e -8xe

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Step 2

Now, the particular solution (P.S) is,

(D2 -6D+5)y 35e -8xe3
35e-8xe
P.S
-3x
(D2 6D 5)
35e3
8xe
(D -6D+5) (D -6D+5)
P.S (P.S,-P.S),
35e
(D -6D+5)
Now,(P.S)
Put D -3
35e
|(P.S),
((-3)-6(-3)+5)
35e
(9+18+5)
35e
32
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(D2 -6D+5)y 35e -8xe3 35e-8xe P.S -3x (D2 6D 5) 35e3 8xe (D -6D+5) (D -6D+5) P.S (P.S,-P.S), 35e (D -6D+5) Now,(P.S) Put D -3 35e |(P.S), ((-3)-6(-3)+5) 35e (9+18+5) 35e 32

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Step 3

Also, find the (P.S)2...

8re
(P.S)
(D-6D+5)
Replace DD-3
8re
(P.S),
((D-3)-6(D-3)+5)
&re*
(D2 -6D+9-6D+18+5)
8xe
(D2 -12D+32)
&e3
(D-8)(D-4)
&e
D
8 1
4
1
-3x
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8re (P.S) (D-6D+5) Replace DD-3 8re (P.S), ((D-3)-6(D-3)+5) &re* (D2 -6D+9-6D+18+5) 8xe (D2 -12D+32) &e3 (D-8)(D-4) &e D 8 1 4 1 -3x

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