Exercise 9Solve the PDE= 0 such that -0 0satisfying the conditions :i) v and its partial derivatives tend to zero as r+ t0dv= 0 on y = 0.дуii) v = f(x), b) f(x)= re¯a²r?Exercise 6Find the fourier sine transform ofa) f(x) = exp(-ax) and deduces sin(sr)ds =32 + a²2b) f(x) = xe¬a²z²Exercise 7duLet= 2with r > 0, t > 0. Suppose the boundary conditionatu(0, t) = 0 and the initial condition u(r,0) = e-,Vx > 0.Solve the p.d.e using the Sine Fourier Transform.

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Find the fourier sine transform of a) f(x) = exp(-ar) and deduce sin(sz) -ds = 2+a² -az b) f(x)= re' ¬a²z² 2.

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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Question

Exercise 9
Solve the PDE
= 0 such that -0 <r< x and y >0
satisfying the conditions :
i) v and its partial derivatives tend to zero as r+ t0
dv
= 0 on y = 0.
ду
ii) v = f(x),

b) f(x)= re¯a²r?
Exercise 6
Find the fourier sine transform of
a) f(x) = exp(-ax) and deduce
s sin(sr)
ds =
32 + a²
2
b) f(x) = xe¬a²z²
Exercise 7
du
Let
= 2
with r > 0, t > 0. Suppose the boundary condition
at
u(0, t) = 0 and the initial condition u(r,0) = e-,Vx > 0.
Solve the p.d.e using the Sine Fourier Transform.

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