Consider the partial differential equation 2² u du dx² Ət with boundary conditions u(0, ₺) = 0 and 1 |u(π, t) un, t) = 0 for t≥ 0, and the initial condition u(x, 0) = X u(r, t) The general solution that satisfies the boundary conditions is Select one: An Ane-16n²t Select the option that gives the correct method for determining the constants An from the given initial condition. An An An An = = = = - = 4 7 8 T > 4 +x. TT ∞ Σ n=1 TT 1 4 1 8 4 ³/16.* π 4 4 ſ 0 1 4 1 8 4 T T π 7T 1 T) 4 IT T • (-x x X sin(4nx). X (-x + 1/7) sin(4nx) dx -x+¹) sin(4x) dx X (-x+ r) cos(4nx) dx -x+ π) cos(4nx) dx x € (-x+ ²1/7) sin(4x) dx
Consider the partial differential equation 2² u du dx² Ət with boundary conditions u(0, ₺) = 0 and 1 |u(π, t) un, t) = 0 for t≥ 0, and the initial condition u(x, 0) = X u(r, t) The general solution that satisfies the boundary conditions is Select one: An Ane-16n²t Select the option that gives the correct method for determining the constants An from the given initial condition. An An An An = = = = - = 4 7 8 T > 4 +x. TT ∞ Σ n=1 TT 1 4 1 8 4 ³/16.* π 4 4 ſ 0 1 4 1 8 4 T T π 7T 1 T) 4 IT T • (-x x X sin(4nx). X (-x + 1/7) sin(4nx) dx -x+¹) sin(4x) dx X (-x+ r) cos(4nx) dx -x+ π) cos(4nx) dx x € (-x+ ²1/7) sin(4x) dx
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
100%
Transcribed Image Text:Consider the partial differential equation
2² u
du
მ2
Ət
with boundary conditions u(0, ₺) = 0 and
1
|u(π, t)
un,
t) = 0 for t≥ 0, and the initial condition
u(x, 0) = X -x+
The general solution that satisfies the boundary
conditions is
u(r, t)
Select one:
Ane-16n²t
sin(4nx).
Select the option that gives the correct method for
determining the constants An from the given initial
condition.
An
An
An
An
An
=
=
=
=
-
=
4
2
7
8
T
4
∞
Σ
n=1
TT
S
1
T
4
T
4
ſ
0
1
4
π
1
8 4
πT
1 T)
4
4
1
7T
8 4
³/16.*
π
IT
T
• (-x
x
X
X
-x+¹) sin(4x) dx
(T)
(-x+ 1/7) sin(4nx) dx
X
-x+ r) cos(4nx) dx
-x+ π) cos(4nx) dx
X
€ (-x+ ²1/7) sin(4x) dx
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
