3Q.4 Consider the initial-boundary value problem0 0,U: - Uzz = 6x,u(0, t) = u(1,t) = 0, t>0,u(r, 0) = 1,0 0,- Vaa = 0,v(0,t) = v(1, t) = 0, t>0,v(r, 0) = 1- (aæ), 0 0.- Va = 0,v(0, t) = v(1, t) = 0, t> 0,v(r, 0) = 1– (x), 0

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Q.4 Consider the initial-boundary value problem u - u = 6z, u(0, t) = u(1, 1) = 0, t>0, u(r, 0) = 1. 00, 00, U - Vz = 0, v(0,1) = v(1,t) = 0, t>0, v(z, 0) = 1- (z), 00, - t = 0, v(0,1) = v(1,t) = 0, t>0, v(1, 0) = 1- (1), 0

Q.4 Consider the initial-boundary value problem u - u = 6z, u(0, t) = u(1, 1) = 0, t>0, u(r, 0) = 1. 00, 00, U - Vz = 0, v(0,1) = v(1,t) = 0, t>0, v(z, 0) = 1- (z), 00, - t = 0, v(0,1) = v(1,t) = 0, t>0, v(1, 0) = 1- (1), 0

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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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

3
Q.4 Consider the initial-boundary value problem
0 <r<1, t > 0,
U: - Uzz = 6x,
u(0, t) = u(1,t) = 0, t>0,
u(r, 0) = 1,
0 <r<1.
(a) Find a function
boundary value problem
such that u(z, t) = v(x, t) + (a) and
t) satisfies the the initial-
0 <*<1, t >0,
- Vaa = 0,
v(0,t) = v(1, t) = 0, t>0,
v(r, 0) = 1- (aæ), 0<I<1.
(b) Solve the initial-boundary value problem
0 <*<1, t > 0.
- Va = 0,
v(0, t) = v(1, t) = 0, t> 0,
v(r, 0) = 1– (x), 0<r<1.

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