**Problem 5: Initial and Boundary Value Problem**Solve the following initial and boundary value problem:1. $ u_t - 2kt u_{xx} = 0 $, for $ 0 < x < \pi $, $ t > 0 $.2. $ u(0, t) = u(\pi, t) = 0 $, for $ t > 0 $.3. $ u(x, 0) = 2 \sin 2x - 5 \sin 3x $, for $ 0 \leq x \leq \pi $.Here, $ k $ is a positive real number.

The given problem is to find the solution for the initial and boundary value problem partial…

Answered: Problem 5. solve the following initial…

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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Problem 5. solve the following initial and boundary Value Problem U₂ - 2kt lax=0₁ OLULIT, tso l(0₁ t) = u(ITE) = 0₁ tro U(x,0) = 2 pin2x-5 pmm 3x, 06 x ≤. ke is a positive real number.