Question

Let u be the solution to the initial boundary value problem for the Heat Equation ut = 5u'' + 10x - 3 with Mixed boundary conditions u(0) = 0 and u(3) = 0 and with initial condition u(0,x) = 0 The solution u of the problem above, with the conventions given in class, has the form u(x,t) = c * e^(-5t) * sin(sqrt(10)t) * sin(sqrt(10)x) with the normalization conditions C = 1 and w = 1. Find the functions W and the constants c. W(x) = c * sin(sqrt(10)x) CA = 1

Name: let u be the solution to the initial boundary value problem for the heat equation utx5u1x0x03 with mixed boundary conditions ut00 and ut30 and with initial condition u0xx 0 the solution u of 98237
Uploaded: 2023-05-10T04:13:42-08:00
Duration: 3 min 18 s
Channel: Madhur L
Description: let u be the solution to the initial boundary value problem for the heat equation utx5u1x0x03 with mixed boundary conditions ut00 and ut30 and with initial condition u0xx 0 the solution u of 98237

          Let u be the solution to the initial boundary value problem for the Heat Equation
ut = 5u'' + 10x - 3
with Mixed boundary conditions u(0) = 0 and u(3) = 0 and with initial condition
u(0,x) = 0

The solution u of the problem above, with the conventions given in class, has the form
u(x,t) = c * e^(-5t) * sin(sqrt(10)t) * sin(sqrt(10)x)

with the normalization conditions C = 1 and w = 1. Find the functions W and the constants c.

W(x) = c * sin(sqrt(10)x)
CA = 1

let u be the solution to the initial boundary value problem for the heat equation utx5u1x0x03 with mixed boundary conditions ut00 and ut30 and with initial condition u0xx 0 the solution u of 98237

Added by Emily R.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Let u be the solution to the initial boundary value problem for the Heat Equation ut = 5u'' + 10x - 3 with Mixed boundary conditions u(0) = 0 and u(3) = 0 and with initial condition u(0,x) = 0 The solution u of the problem above, with the conventions given in class, has the form u(x,t) = c * e^(-5t) * sin(sqrt(10)t) * sin(sqrt(10)x) with the normalization conditions C = 1 and w = 1. Find the functions W and the constants c. W(x) = c * sin(sqrt(10)x) CA = 1