y be a real constant with 21 for the parametric functional S[x,y] = [[ª dt [√ï³² + 2y àÿ + ij² − \(xÿ−ày)], \>0, with the boundary conditions (0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. dx dy +2 = ds ds 2(c-Ay) and dx dy Υ + ds ds = =2(d+Xx), where c and d are constants and | s(t) = √² dt√√² + 2y ȧy +ÿ². 2 dx dx dy dy 2 +27 + = 1. ds ds ds ds (1-2)x' = D-X where D = 2(c-yd), X = 2X(yx + y), C+Y where C = 2(dyc), Y = 2λ(x + y), (1-2) where dx I' = ds y' dy = ds X2 Y2-2yXY - 4c(1-2)X+4d(1-2)Y +C2D2+2yCD = (1-2)2.
y be a real constant with 21 for the parametric functional S[x,y] = [[ª dt [√ï³² + 2y àÿ + ij² − \(xÿ−ày)], \>0, with the boundary conditions (0) = y(0) = 0, x(1) = R > 0 and y(1) = 0. dx dy +2 = ds ds 2(c-Ay) and dx dy Υ + ds ds = =2(d+Xx), where c and d are constants and | s(t) = √² dt√√² + 2y ȧy +ÿ². 2 dx dx dy dy 2 +27 + = 1. ds ds ds ds (1-2)x' = D-X where D = 2(c-yd), X = 2X(yx + y), C+Y where C = 2(dyc), Y = 2λ(x + y), (1-2) where dx I' = ds y' dy = ds X2 Y2-2yXY - 4c(1-2)X+4d(1-2)Y +C2D2+2yCD = (1-2)2.
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
use the boundary conditions to show that C=−λR.
![y be a real constant with 21 for the parametric functional
S[x,y] = [[ª dt [√ï³² + 2y àÿ + ij² − \(xÿ−ày)], \>0,
with the boundary conditions (0) = y(0) = 0, x(1) = R > 0 and y(1) = 0.
dx dy
+2 =
ds ds
2(c-Ay) and
dx dy
Υ +
ds ds
=
=2(d+Xx),
where c and d are constants and
| s(t) = √²
dt√√² + 2y ȧy +ÿ².
2
dx
dx dy dy
2
+27
+
= 1.
ds
ds ds
ds
(1-2)x' = D-X where D = 2(c-yd), X = 2X(yx + y),
C+Y where C = 2(dyc), Y = 2λ(x + y),
(1-2)
where
dx
I'
=
ds
y'
dy
=
ds
X2 Y2-2yXY - 4c(1-2)X+4d(1-2)Y
+C2D2+2yCD = (1-2)2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6c8ed7d-75cc-4e27-869e-3ad6a1efc0b4%2F9ef37a23-58bd-4227-a64b-fbb6f282df8f%2F8eeuqg_processed.png&w=3840&q=75)
Transcribed Image Text:y be a real constant with 21 for the parametric functional
S[x,y] = [[ª dt [√ï³² + 2y àÿ + ij² − \(xÿ−ày)], \>0,
with the boundary conditions (0) = y(0) = 0, x(1) = R > 0 and y(1) = 0.
dx dy
+2 =
ds ds
2(c-Ay) and
dx dy
Υ +
ds ds
=
=2(d+Xx),
where c and d are constants and
| s(t) = √²
dt√√² + 2y ȧy +ÿ².
2
dx
dx dy dy
2
+27
+
= 1.
ds
ds ds
ds
(1-2)x' = D-X where D = 2(c-yd), X = 2X(yx + y),
C+Y where C = 2(dyc), Y = 2λ(x + y),
(1-2)
where
dx
I'
=
ds
y'
dy
=
ds
X2 Y2-2yXY - 4c(1-2)X+4d(1-2)Y
+C2D2+2yCD = (1-2)2.
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