Find the general solution to the non-homogeneous equation: y^('')+8y^(') + 25y = cos(2x).
Find the general solution to the non-homogeneous equation: y^('')+8y^(') + 25y = cos(2x).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Find the general solution to the non-homogeneous equation: y^('')+8y^(') + 25y = cos(2x).
![th-
tl-
X170 - 1 (1x2-X11³0 / (x²+x-10
(X!-XD)
th-
((XU1²S + 2 + 1/500 6) + ² = = 16
=f
d =
X-XP
62
(1-6)11-1)
1-1/2
XP (1) X₁1E-² SXILE+#+2) : (1²)|
хр
= dh
S
11-8-7
= XP₂ X11² #P²
xp
| √6
(1 E-1)+() =
x²₂0 = | 11 | 1² || X²E+X50) = Xx!2@ |-{I(! E−b−) +()
(1-1-)
x²y³ = xp x² 5 + XP x-xed S
XP X²20 · X1 E-p-1³ S X₁1E+) = x²20 L/I (E-b-) + ( )
X11E-$-)!
XL
+-}+Q]O_{TIE+-7-h
0=96+68+h
X!2ª } - ( I (!E-} − ) + ( ) 0 ₁ _ (I (!E+Þ — ) - ( )
(X8/50) = 652+√√8+₁1613
0= with
1x|u²5+1X150) E= = load of
(X) U1²S + (X)/50) { = = h
(MUS+SO) (E-) = th](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe742bcfc-6571-4eb6-8020-0d244ddd1492%2Fa64fece2-aa28-425f-a2e3-eeb4ecc4aab2%2Fub2ggwj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:th-
tl-
X170 - 1 (1x2-X11³0 / (x²+x-10
(X!-XD)
th-
((XU1²S + 2 + 1/500 6) + ² = = 16
=f
d =
X-XP
62
(1-6)11-1)
1-1/2
XP (1) X₁1E-² SXILE+#+2) : (1²)|
хр
= dh
S
11-8-7
= XP₂ X11² #P²
xp
| √6
(1 E-1)+() =
x²₂0 = | 11 | 1² || X²E+X50) = Xx!2@ |-{I(! E−b−) +()
(1-1-)
x²y³ = xp x² 5 + XP x-xed S
XP X²20 · X1 E-p-1³ S X₁1E+) = x²20 L/I (E-b-) + ( )
X11E-$-)!
XL
+-}+Q]O_{TIE+-7-h
0=96+68+h
X!2ª } - ( I (!E-} − ) + ( ) 0 ₁ _ (I (!E+Þ — ) - ( )
(X8/50) = 652+√√8+₁1613
0= with
1x|u²5+1X150) E= = load of
(X) U1²S + (X)/50) { = = h
(MUS+SO) (E-) = th
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That was not what I asked for. I wanted you to solve the problem using the method using the Image that I uploaded. Find the general solution to y^('') + 8y^(') + 25y = cos(2x).
![th-
tl-
X170 - 1 (1x2-X11³0 / (x²+x-10
(X!-XD)
th-
((XU1²S + 2 + 1/500 6) + ² = = 16
=f
d =
X-XP
62
(1-6)11-1)
1-1/2
XP (1) X₁1E-² SXILE+#+2) : (1²)|
хр
= dh
S
11-8-7
= XP₂ X11² #P²
xp
| √6
(1 E-1)+() =
x²₂0 = | 11 | 1² || X²E+X50) = Xx!2@ |-{I(! E−b−) +()
(1-1-)
x²y³ = xp x² 5 + XP x-xed S
XP X²20 · X1 E-p-1³ S X₁1E+) = x²20 L/I (E-b-) + ( )
X11E-$-)!
XL
+-}+Q]O_{TIE+-7-h
0=96+68+h
X!2ª } - ( I (!E-} − ) + ( ) 0 ₁ _ (I (!E+Þ — ) - ( )
(X8/50) = 652+√√8+₁1613
0= with
1x|u²5+1X150) E= = load of
(X) U1²S + (X)/50) { = = h
(MUS+SO) (E-) = th](https://content.bartleby.com/qna-images/question/e742bcfc-6571-4eb6-8020-0d244ddd1492/cf15b5d3-498b-4f42-beb8-25b4d8fe0d3c/imkgnn_processed.jpeg)
Transcribed Image Text:th-
tl-
X170 - 1 (1x2-X11³0 / (x²+x-10
(X!-XD)
th-
((XU1²S + 2 + 1/500 6) + ² = = 16
=f
d =
X-XP
62
(1-6)11-1)
1-1/2
XP (1) X₁1E-² SXILE+#+2) : (1²)|
хр
= dh
S
11-8-7
= XP₂ X11² #P²
xp
| √6
(1 E-1)+() =
x²₂0 = | 11 | 1² || X²E+X50) = Xx!2@ |-{I(! E−b−) +()
(1-1-)
x²y³ = xp x² 5 + XP x-xed S
XP X²20 · X1 E-p-1³ S X₁1E+) = x²20 L/I (E-b-) + ( )
X11E-$-)!
XL
+-}+Q]O_{TIE+-7-h
0=96+68+h
X!2ª } - ( I (!E-} − ) + ( ) 0 ₁ _ (I (!E+Þ — ) - ( )
(X8/50) = 652+√√8+₁1613
0= with
1x|u²5+1X150) E= = load of
(X) U1²S + (X)/50) { = = h
(MUS+SO) (E-) = th
Solution
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