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 theazuforma²uc22 ди'spherical wave equation. Change the variables v = ru to get ther ar.a?vfollowing PDE for v:= c2ar2at2дх7) Solve the partial differential equation by using the method of integration:at= t e2t giventhat t = 0, x = 3eº. Explain the procedure followed in your own words.

Given , 5) F(s) is the complex Fourier transform of the function f(x) 6) A spherical wave is a…

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

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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