Please solve only question no 3 Description1. 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 conditionsu(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 conditionsu(x, 0) = 0 if x < 0 and = e-2x if x > 0. for x and t on real axis, and no boundary conditions.

Given heat diffusion equation is ∂2u∂x2-∂u∂t=0 or ∂u∂t-∂2u∂x2=0 (1) with initial…

Answered: 3. Using the Fourier transform method…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

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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.