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3. Using the Fourier transform method solve the heat diffusion PDE equation - = 0 with initial Cauchy conditions u(x, 0) = 0 if x < 0 and = e-2x if x > 0, for x and t on real axis, and no boundary conditions.

3. Using the Fourier transform method solve the heat diffusion PDE equation - = 0 with initial Cauchy conditions u(x, 0) = 0 if x < 0 and = e-2x if x > 0, for x and t on real axis, and no boundary conditions.

Advanced Engineering Mathematics
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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Please solve only question no 3

Description 1. Using the Fourier transform method solve the ODE: y"(t)+8 y'(t)+25 y(t)=sin(t) without any initial conditions for any t real. 2. Using the Fourier transform method solve the wave PDE equation - 1 = 0 with initial Cauchy conditions u(x, 0) = sin(x), (x, 0) = 0 for x and t on real axis, and no boundary conditions. 3. Using the Fourier transform method solve the heat diffusion PDE equation = 0 with initial Cauchy conditions u(x, 0) = 0 if x < 0 and = e-2x if x > 0. for x and t on real axis, and no boundary conditions.
Transcribed Image Text:Description 1. Using the Fourier transform method solve the ODE: y"(t)+8 y'(t)+25 y(t)=sin(t) without any initial conditions for any t real. 2. Using the Fourier transform method solve the wave PDE equation - 1 = 0 with initial Cauchy conditions u(x, 0) = sin(x), (x, 0) = 0 for x and t on real axis, and no boundary conditions. 3. Using the Fourier transform method solve the heat diffusion PDE equation = 0 with initial Cauchy conditions u(x, 0) = 0 if x < 0 and = e-2x if x > 0. for x and t on real axis, and no boundary conditions.
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