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9. Our goal is to find all solutions of the partial differential equation uyy = 2xz that satisfy certain conditions. (a) First, integrate twice to determine a general expression for u(x, y, z) (so, u(x, yz) = ...). (b) Next, determine for what functions the solution you found in (a) satisfies u(x, 0, z) = 0 and u(x, π, z) = z cos x, thereby obtaining the solution to the problem Uyy = 2xz, u(x, 0, z) = 0, u(x, π, z) = z cos x. (c) Verify that your solution in (b) solves the equation. (For example, if I want to verify that x = 2 solves 3+ x = 5, I would substitute 2 in for x and make sure that I get 5 on both sides of the equation.)

9. Our goal is to find all solutions of the partial differential equation uyy = 2xz that satisfy certain conditions. (a) First, integrate twice to determine a general expression for u(x, y, z) (so, u(x, yz) = ...). (b) Next, determine for what functions the solution you found in (a) satisfies u(x, 0, z) = 0 and u(x, π, z) = z cos x, thereby obtaining the solution to the problem Uyy = 2xz, u(x, 0, z) = 0, u(x, π, z) = z cos x. (c) Verify that your solution in (b) solves the equation. (For example, if I want to verify that x = 2 solves 3+ x = 5, I would substitute 2 in for x and make sure that I get 5 on both sides of the equation.)

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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9. Our goal is to find all solutions of the partial differential equation uyy = 2xz that satisfy certain conditions. (a) First, integrate twice to determine a general expression for u(x, y, z) (so, u(x, yz) = ...). (b) Next, determine for what functions the solution you found in (a) satisfies u(x, 0, z) = 0 and u(x, 7, z) = z cos x, thereby obtaining the solution to the problem Uyy = 2xz, u(x, 0, z) = 0, u(x, π, z) = z cos x. (c) Verify that your solution in (b) solves the equation. (For example, if I want to verify that x = 2 solves 3+ x = 5, I would substitute 2 in for x and make sure that I get 5 on both sides of the equation.)
Transcribed Image Text:9. Our goal is to find all solutions of the partial differential equation uyy = 2xz that satisfy certain conditions. (a) First, integrate twice to determine a general expression for u(x, y, z) (so, u(x, yz) = ...). (b) Next, determine for what functions the solution you found in (a) satisfies u(x, 0, z) = 0 and u(x, 7, z) = z cos x, thereby obtaining the solution to the problem Uyy = 2xz, u(x, 0, z) = 0, u(x, π, z) = z cos x. (c) Verify that your solution in (b) solves the equation. (For example, if I want to verify that x = 2 solves 3+ x = 5, I would substitute 2 in for x and make sure that I get 5 on both sides of the equation.)
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