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Consider the following PDE with three independent variables: 10² y Oy² ди Ət 10²u x əx² + Separate variables with u(x, y, t) = f(x)g(y)h(t) to derive ODEs for each of f, g, and h. Do NOT attempt to solve the resulting ODEs. Also, you do not have to separate the variables all at once; you may separate them one at a time if you prefer.

Consider the following PDE with three independent variables: 10² y Oy² ди Ət 10²u x əx² + Separate variables with u(x, y, t) = f(x)g(y)h(t) to derive ODEs for each of f, g, and h. Do NOT attempt to solve the resulting ODEs. Also, you do not have to separate the variables all at once; you may separate them one at a time if you prefer.

Advanced Engineering Mathematics
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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Consider the following PDE with three independent variables: 102 10² x 0x² y dy² ди Ət + Separate variables with u(x, y, t) = f(x)g(y)h(t) to derive ODEs for each of f, g, and h. Do NOT attempt to solve the resulting ODEs. Also, you do not have to separate the variables all at once; you may separate them one at a time if you prefer.
Transcribed Image Text:Consider the following PDE with three independent variables: 102 10² x 0x² y dy² ди Ət + Separate variables with u(x, y, t) = f(x)g(y)h(t) to derive ODEs for each of f, g, and h. Do NOT attempt to solve the resulting ODEs. Also, you do not have to separate the variables all at once; you may separate them one at a time if you prefer.
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