U(x, t) = 4,(x, t), 00 u,(0, t) = 0, u,(1, t) = 0, u(x,0) = cos 2mx, 4, (x,0) = -2m cOs TX %3D
U(x, t) = 4,(x, t), 00 u,(0, t) = 0, u,(1, t) = 0, u(x,0) = cos 2mx, 4, (x,0) = -2m cOs TX %3D
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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
Using seperation of variable method to solve question no 4.
Transcribed Image Text:Classify and solve the following PDE's by separation of variable method.
QNo 3:
4,(y. t) = ku,,y. t),
0<y < L,t >0
u(0, t) = 0,
u,(L, t) + hu(L, t) = 0, u(y,0) = f(y)
Q.No.4
U(x, t) = u (x, t),
0<x<1,t > 0
u, (0, t) = 0,
u(1,t) = 0, u(x, 0) = cos 2mx,
14, (x,0) = -2n cos TX
Expert Solution
Step 1
In this question, we solve the boundary value problem by using the method of variable seperation
i.e.
the possible steps are defined in Step 2.
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