Question

Use the method of separation of variables to solve the heat equation $\frac{\partial u}{\partial t} = 4 \frac{\partial^2 u}{\partial x^2}$ with the boundary conditions u(0,t) = 0, u<sub>x</sub>(1,t) = 0, t > 0 and the initial condition u(x, 0) = 1 - x, 0 < x < 1.

          Use the method of separation of variables to solve the heat equation
$\frac{\partial u}{\partial t} = 4 \frac{\partial^2 u}{\partial x^2}$
with the boundary conditions
u(0,t) = 0, u<sub>x</sub>(1,t) = 0, t > 0
and the initial condition
u(x, 0) = 1 - x, 0 < x < 1.

Use the method of separation of variables to solve the heat equation
(∂ u)/(∂ t) = 4 (∂^2 u)/(∂ x^2)
with the boundary conditions
u(0,t) = 0, u<sub>x</sub>(1,t) = 0, t > 0
and the initial condition
u(x, 0) = 1 - x, 0 < x < 1.

Added by Kristine J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

02/20/2023

Step 1

So, we assume that u(x,t) = X(x)T(t). Show more…

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please answer the question base on topic Partial Differential Equations in th solution🥺 please give the complete solution Use the method of separation of variables to solve the heat equation du 02u ne ax2 with the boundary conditions u0,t=0,u1,t=0,t>0 and the initial condition ux,0=1-x,0<x<1.