Answered: Classify and solve the following PDE's…

Math

Advanced Math

Classify and solve the following PDE's by separation of variable method.

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

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

By using separation of variable method to solve this problem

Classify and solve the following PDE's by separation of variable method.
QNo 3:
(4.5)
0<y< L, t >0
u, (L, t) + hu(L, t) = 0, u(y,0) = f)
4,(y, t) = ku,y(y, t),
u(0, t) = 0,

Expert Solution

Step 1

In this question, we have to solve the partial differential equation by using the variable separation method.

Let $U (y, t) = Y (y) . T (t)$

Step by step

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