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Consider the following PDE 2 ðu + 2²0u = 2ry? ду (i) Find the general solution to this PDE.

Consider the following PDE 2 ðu + 2²0u = 2ry? ду (i) Find the general solution to this PDE.

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 ди + x2! 2xy? he (i) Find the general solution to this PDE. exp(у®) (ii) Show that the particular solution to this PDE if you are given that u(0, y) and u(x,0) = x² + exp(-x³) is u(x, y) = x² + exp(y* – x*) ii) What is the particular solution to this PDE if now you are given that u(0, y) = -yº and и(х, 0) — х? —26?
Transcribed Image Text:Consider the following PDE ди + x2! 2xy? he (i) Find the general solution to this PDE. exp(у®) (ii) Show that the particular solution to this PDE if you are given that u(0, y) and u(x,0) = x² + exp(-x³) is u(x, y) = x² + exp(y* – x*) ii) What is the particular solution to this PDE if now you are given that u(0, y) = -yº and и(х, 0) — х? —26?
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