Hence, or otherwise, show that the solution of d²y dx² dy dx is 2 sinh t y = 2 sin sin ( substitution - 2 cosh x +ysinh*r=0, g(1) = 0, g(2) = 2, (cosh x cosh 1) (cosh 2 - cosh 1)) - this is a solution by direct
Hence, or otherwise, show that the solution of d²y dx² dy dx is 2 sinh t y = 2 sin sin ( substitution - 2 cosh x +ysinh*r=0, g(1) = 0, g(2) = 2, (cosh x cosh 1) (cosh 2 - cosh 1)) - this is a solution by direct
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Consider the functional
S[2] = [
is
dc [ u sinh x
2 sinh x
y =
Hence, or otherwise, show that the solution of
dy
d²y
dx²
dx
2 sin
مردم
sin
substitution
2y/²
sinh x
- 2 cosh x
(cosh x
(cosh 2
√2
"
cosh 1)
y(a) = A, y(b) = B, 0 < a < b.
+ysinh®æ=0, g(1)=0, y(2) = 2,
cosh 1)
this is a solution by direct](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2F38446124-fd64-4d30-b842-516c5b3eaf9c%2Fdmcpj1c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the functional
S[2] = [
is
dc [ u sinh x
2 sinh x
y =
Hence, or otherwise, show that the solution of
dy
d²y
dx²
dx
2 sin
مردم
sin
substitution
2y/²
sinh x
- 2 cosh x
(cosh x
(cosh 2
√2
"
cosh 1)
y(a) = A, y(b) = B, 0 < a < b.
+ysinh®æ=0, g(1)=0, y(2) = 2,
cosh 1)
this is a solution by direct
![Ş[y] = { L (xi y₁, y¹) dx : ;; 2= yt sin x
het
Euler- Lagrange Equation =
24- & (3)
Zysin x = 0
• coshx
ay'
u.=
= 0
2
y 'exs = di d
24 = 2y sinx
ay
then du = sinhx dx
year = A₁ y cb₁ = B₁ocacb.
you yếu sinh x
S[y] = (a (y² = 24/² =) sinhx dx
sinh
•Sinhb
Sinha (y² = 2 (y kus szrch x)²) daxi
si
sinh
Isinha:
Hence, the new.
•Sinhb
- Socha (y^² - 12/18 (19) ²); where un = simha
sinh
· U₂ =
sinh bị
independent variable is
•coshx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59d44c96-efb1-4f3c-83b3-5a6a84cf94cb%2F38446124-fd64-4d30-b842-516c5b3eaf9c%2F8w91fre_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Ş[y] = { L (xi y₁, y¹) dx : ;; 2= yt sin x
het
Euler- Lagrange Equation =
24- & (3)
Zysin x = 0
• coshx
ay'
u.=
= 0
2
y 'exs = di d
24 = 2y sinx
ay
then du = sinhx dx
year = A₁ y cb₁ = B₁ocacb.
you yếu sinh x
S[y] = (a (y² = 24/² =) sinhx dx
sinh
•Sinhb
Sinha (y² = 2 (y kus szrch x)²) daxi
si
sinh
Isinha:
Hence, the new.
•Sinhb
- Socha (y^² - 12/18 (19) ²); where un = simha
sinh
· U₂ =
sinh bị
independent variable is
•coshx.
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