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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.

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.

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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**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.
Transcribed Image Text:**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.
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