Question

2. Find the solution $u = u(x, t)$ to the heat equation $$ \frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2} $$ where $u$ is subject to the following boundary and initial conditions $$ u(0, t) = u(1, t), \quad u_x(0, t) = u_x(1, t) $$ $$ u(x, 0) = 1 - x $$

Name: 2 find the solution u ux t to the heat equation fracpartial upartial t k fracpartial2 upartial x2 where u is subject to the following boundary and initial conditions u0 t u1 t quad ux0 t u 50846
Uploaded: 2022-01-06T08:27:28-08:00
Duration: 2 min 6 s
Channel: Hast Aggarwal
Description: 2 find the solution u ux t to the heat equation fracpartial upartial t k fracpartial2 upartial x2 where u is subject to the following boundary and initial conditions u0 t u1 t quad ux0 t u 50846

          2. Find the solution $u = u(x, t)$ to the heat equation
$$
\frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2}
$$
where $u$ is subject to the following boundary and initial conditions
$$
u(0, t) = u(1, t), \quad u_x(0, t) = u_x(1, t)
$$
$$
u(x, 0) = 1 - x
$$

$2 find the solution u ux t to the heat equation fracpartial upartial t k fracpartial2 upartial x2 where u is subject to the following boundary and initial conditions u0 t u1 t quad ux0 t u 50846$

Added by Cristian J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hast Aggarwal

01/06/2022

Step 1

Step 1: We are given the heat equation $$ \frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2} $$ with boundary conditions $$ u(0, t) = u(1, t), \quad u_x(0, t) = u_x(1, t) $$ and initial condition $$ u(x, 0) = 1 - x $$ Show more…

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2. Find the solution $u = u(x, t)$ to the heat equation $$ \frac{\partial u}{\partial t} = k \frac{\partial^2 u}{\partial x^2} $$ where $u$ is subject to the following boundary and initial conditions $$ u(0, t) = u(1, t), \quad u_x(0, t) = u_x(1, t) $$ $$ u(x, 0) = 1 - x $$