12 2 5[1₁ Y>] = {dx [74, ² + 24 y/y + z\y 2² +4y² ² + 12yy₁ + 99² ² ] Euler - Lagrange equations for y, and you are £ (148 + 24y² )-(84, +12g2) = and » &yır + 144" - 44, -6y2 =0 and (>4y² + +2y) - (12y + 18y2) = 0 ⇒ 14y, +244" - Sy₁ - 12y2 =0 7y" + 12y" -4y, - byz and → 24 y " + 42 yu - 124, -18y2=0 =0 , = 0 4₁ =α31-332 y₁ = αzí - 3gr → 4y₁ + 7y," -241-342- , уг = 31 +ъзг Yi 81+232 y = gì tước y! S[31, 32] = [dx [7 (231 -336)² + 24 (231 - 336) (31 +286) + = ye + 21 (z 1 + zzz² )² + 4 (α281-332)² + 12 (α81-332) (31 +232) +9 (317232) ³] 92 Yi "" Solo [7 (dit - 6αzízé + 932²) + 24(231²+243√32-38132-635) + 21 (g₁² + 4 zizi +4z²² ) + 4 (2}; - 6α132 + 932) +12 (237 + 2x182–81h2 – 632) + 9 (z; +4zizz + 435 ) ] -623132 What is L 22 How to find α ??
12 2 5[1₁ Y>] = {dx [74, ² + 24 y/y + z\y 2² +4y² ² + 12yy₁ + 99² ² ] Euler - Lagrange equations for y, and you are £ (148 + 24y² )-(84, +12g2) = and » &yır + 144" - 44, -6y2 =0 and (>4y² + +2y) - (12y + 18y2) = 0 ⇒ 14y, +244" - Sy₁ - 12y2 =0 7y" + 12y" -4y, - byz and → 24 y " + 42 yu - 124, -18y2=0 =0 , = 0 4₁ =α31-332 y₁ = αzí - 3gr → 4y₁ + 7y," -241-342- , уг = 31 +ъзг Yi 81+232 y = gì tước y! S[31, 32] = [dx [7 (231 -336)² + 24 (231 - 336) (31 +286) + = ye + 21 (z 1 + zzz² )² + 4 (α281-332)² + 12 (α81-332) (31 +232) +9 (317232) ³] 92 Yi "" Solo [7 (dit - 6αzízé + 932²) + 24(231²+243√32-38132-635) + 21 (g₁² + 4 zizi +4z²² ) + 4 (2}; - 6α132 + 932) +12 (237 + 2x182–81h2 – 632) + 9 (z; +4zizz + 435 ) ] -623132 What is L 22 How to find α ??
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
![12
2
5[1₁ Y>] = {dx [74, ² + 24 y/y + z\y 2² +4y² ² + 12yy₁ + 99² ² ]
Euler - Lagrange equations for y, and you are
£ (148 + 24y² )-(84, +12g2) =
and » &yır + 144" - 44, -6y2 =0
and
(>4y² + +2y) - (12y + 18y2) = 0
⇒
14y, +244" - Sy₁ - 12y2 =0
7y" + 12y" -4y, - byz
and
→ 24 y " + 42 yu
-
124, -18y2=0
=0
,
= 0
4₁ =α31-332
y₁ = αzí - 3gr
→ 4y₁ + 7y," -241-342-
, уг = 31 +ъзг
Yi
81+232
y = gì tước
y!
S[31, 32] = [dx [7 (231 -336)² + 24 (231 - 336) (31 +286) +
=
ye + 21 (z 1 + zzz² )² + 4 (α281-332)² + 12 (α81-332) (31 +232)
+9 (317232) ³]
92
Yi
""
Solo [7 (dit - 6αzízé + 932²) + 24(231²+243√32-38132-635)
+ 21 (g₁² + 4 zizi +4z²² ) + 4 (2}; - 6α132 + 932)
+12 (237 + 2x182–81h2 – 632) + 9 (z; +4zizz + 435 ) ]
-623132
What
is
L
22
How to find α ??](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c8ed7d-75cc-4e27-869e-3ad6a1efc0b4%2F8e45da4b-e93f-46d9-9b16-8332475a58ac%2Forapzot_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12
2
5[1₁ Y>] = {dx [74, ² + 24 y/y + z\y 2² +4y² ² + 12yy₁ + 99² ² ]
Euler - Lagrange equations for y, and you are
£ (148 + 24y² )-(84, +12g2) =
and » &yır + 144" - 44, -6y2 =0
and
(>4y² + +2y) - (12y + 18y2) = 0
⇒
14y, +244" - Sy₁ - 12y2 =0
7y" + 12y" -4y, - byz
and
→ 24 y " + 42 yu
-
124, -18y2=0
=0
,
= 0
4₁ =α31-332
y₁ = αzí - 3gr
→ 4y₁ + 7y," -241-342-
, уг = 31 +ъзг
Yi
81+232
y = gì tước
y!
S[31, 32] = [dx [7 (231 -336)² + 24 (231 - 336) (31 +286) +
=
ye + 21 (z 1 + zzz² )² + 4 (α281-332)² + 12 (α81-332) (31 +232)
+9 (317232) ³]
92
Yi
""
Solo [7 (dit - 6αzízé + 932²) + 24(231²+243√32-38132-635)
+ 21 (g₁² + 4 zizi +4z²² ) + 4 (2}; - 6α132 + 932)
+12 (237 + 2x182–81h2 – 632) + 9 (z; +4zizz + 435 ) ]
-623132
What
is
L
22
How to find α ??
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