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6) A spherical wave is a solution of the three-dimensional wave equation of the form u(r, t), where r is the distance to the origin (the spherical coordinate). The wave equation takes the ra²u, 2 du form spherical wave equation. Change the variables v = ru to get the following PDE for v: at2 = c2 ax 7) Solve the partial differential equation by using the method of integration: = t e2t given that t = 0, x = 3e'. Explain the procedure followed in your own words. %3D

6) A spherical wave is a solution of the three-dimensional wave equation of the form u(r, t), where r is the distance to the origin (the spherical coordinate). The wave equation takes the ra²u, 2 du form spherical wave equation. Change the variables v = ru to get the following PDE for v: at2 = c2 ax 7) Solve the partial differential equation by using the method of integration: = t e2t given that t = 0, x = 3e'. Explain the procedure followed in your own words. %3D

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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5) If F(s) is the complex Fourier transform of the function f(x), then prove that F{f(x – a)} = e-ias F(s). 6) A spherical wave is a solution of the three-dimensional wave equation of the form u(r, t), where r is the distance to the origin (the spherical coordinate). The wave equation takes the azu form a²u c2 2 ди' spherical wave equation. Change the variables v = ru to get the r ar. a?v following PDE for v: = c2 ar2 at2 дх 7) Solve the partial differential equation by using the method of integration: at = t e2t given that t = 0, x = 3eº. Explain the procedure followed in your own words.
Transcribed Image Text:5) If F(s) is the complex Fourier transform of the function f(x), then prove that F{f(x – a)} = e-ias F(s). 6) A spherical wave is a solution of the three-dimensional wave equation of the form u(r, t), where r is the distance to the origin (the spherical coordinate). The wave equation takes the azu form a²u c2 2 ди' spherical wave equation. Change the variables v = ru to get the r ar. a?v following PDE for v: = c2 ar2 at2 дх 7) Solve the partial differential equation by using the method of integration: at = t e2t given that t = 0, x = 3eº. Explain the procedure followed in your own words.
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