A Solution to a PDE and BCsDetermine the complete solution to the heat equationди(х, 1)ô²u(x,t)ôx?2 =for 0 < x < 1 and 0 < t, given the boundary conditionsu(0,г) 3D 0andu(1,t) = 0for all 0 < t, and the initial condition u(x,0) = x² for 0 < x < 1. You may use the fact that[x sin(ax)dxsin(ax) – (ax) cos(ax)a?Sxcos(ax)dxcos(ax)+ (ax) sin(ax)a?andfor a + 0.

Given, ∂2u(x,t)∂x2−2=∂u(x,t)∂t, 0<x<1 and t>0with the boundary conditions u(x,0)=0 and…

Answered: Determine the complete solution to the…

Math

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Determine the complete solution to the heat equation ди(х, ) a²u(x,t) for 0

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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Concept explainers

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

A Solution to a PDE and BCs
Determine the complete solution to the heat equation
ди(х, 1)
ô²u(x,t)
ôx?
2 =
for 0 < x < 1 and 0 < t, given the boundary conditions
u(0,г) 3D 0
and
u(1,t) = 0
for all 0 < t, and the initial condition u(x,0) = x² for 0 < x < 1. You may use the fact that
[x sin(ax)dx
sin(ax) – (ax) cos(ax)
a?
Sxcos(ax)dx
cos(ax)+ (ax) sin(ax)
a?
and
for a + 0.

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