Solve the following boundary value problem. ut=9uxx, 0 0; u, (0,t) ux (3,t) = 0, u(x,0) = 9 cos O A. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers, using as needed.) O B. O C. O D. ao The solution is of the form u(x,t) = + 2 u(x,t) = u(x,t) = COS TX u(x,t) = The solution is of the form u(x,t) = b₁ exp n=1 sin 3xx. sin ™X- u(x,t)= cos 3xx. 00 The solution is of the form u(x,t) = Σb, exp n=1 cos 3Tx. cos TX- 00 cos The solution is of the form u(x,t) = 2 Σ an exp n=1 ao cos (²3TX) ∞ + 2 an exp n=1 (22) (TX) nkt nлx L n2 KỈ 2 sin - 5 cos sin nkt COS nxx L Μπχ L cos where L= where L = where L = ΠπΧ L , k = , where L= k= , b₂ = , b₁ = k= ao = , b4= b3 = , ao = a₁ = a3 = and bn = and b₁ = a₂ = a4= and an = otherwise. The solution is otherwise. The solution is otherwise. The solution is , and an = otherwise. The solution is
Solve the following boundary value problem. ut=9uxx, 0 0; u, (0,t) ux (3,t) = 0, u(x,0) = 9 cos O A. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers, using as needed.) O B. O C. O D. ao The solution is of the form u(x,t) = + 2 u(x,t) = u(x,t) = COS TX u(x,t) = The solution is of the form u(x,t) = b₁ exp n=1 sin 3xx. sin ™X- u(x,t)= cos 3xx. 00 The solution is of the form u(x,t) = Σb, exp n=1 cos 3Tx. cos TX- 00 cos The solution is of the form u(x,t) = 2 Σ an exp n=1 ao cos (²3TX) ∞ + 2 an exp n=1 (22) (TX) nkt nлx L n2 KỈ 2 sin - 5 cos sin nkt COS nxx L Μπχ L cos where L= where L = where L = ΠπΧ L , k = , where L= k= , b₂ = , b₁ = k= ao = , b4= b3 = , ao = a₁ = a3 = and bn = and b₁ = a₂ = a4= and an = otherwise. The solution is otherwise. The solution is otherwise. The solution is , and an = otherwise. The solution is
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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Transcribed Image Text:Solve the following boundary value problem.
u₁=9uxx, 0<x<3, t> 0; ux (0,t) = ux (3,t) = 0, u(x,0) = 9 cos
O A.
B.
O C.
Select the correct choice below and fill in the answer boxes to complete your choice.
(Type exact answers, using as needed.)
O D.
The solution is of the form u(x,t) =
2
u(x,t) =
u(x,t)=
e
u(x,t) =
e
COS TX-
The solution is of the form u(x,t) = b exp
n=1
e
sin TX-
e cos 3лx.
COS TX-
e
+
The solution is of the form u(x,t) = b exp
e
sin 3tx.
∞
Σ an exp
n=1
cos 3лx.
ao
==
The solution is of the form u(x,t) =
+
2
(3²=₁X) -
2|3
4
U(XI) = 008 (3)- cos (7²).
u(x,t)
COS
COS
3
∞
Σ an exp
n=1
-TX - 5 cos
-n²π²kt
L²
-n²
L²
2
∞
- t
· Σ - - - - - -)
sin
n=1
KÍ
sin
COS
4
(37TX)
nox
nлx
|-
"
(-2)-(7)
COS
L²
where L =
where L =
where L =
k=, b₂ =
k=
, k =
where L =
₁b₁ =
k=
ao
"
=
b4 =
b3
ao =
=
=
₁: az
"
J
and bn
=
and bn
a₂ =
=
=
a4 =
and an
=
otherwise. The solution is
and an
otherwise. The solution is
otherwise. The solution is
=
otherwise. The solution is
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