1. (i) The functions u(x, y) and v(x, y) satisfy the following system of partial differential equations for y x2 3y? 2.xu, + (y + x²)uy + (y – x²)v, = (y – x²) ( 2y x3 Зу? 2av, + (y – x²)uy + (y + x²)vy = (y – x²) ( 2y – x² + x3 | Show that this system is hyperbolic with the characteristics V = Y – 2
1. (i) The functions u(x, y) and v(x, y) satisfy the following system of partial differential equations for y x2 3y? 2.xu, + (y + x²)uy + (y – x²)v, = (y – x²) ( 2y x3 Зу? 2av, + (y – x²)uy + (y + x²)vy = (y – x²) ( 2y – x² + x3 | Show that this system is hyperbolic with the characteristics V = Y – 2
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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Transcribed Image Text:1. (i) The functions u(x, y) and v(x, y) satisfy the following system of partial
differential equations for y + x²
2xu, + (y + x²)u,y + (y – x²)vy = (y – x²) ( 2y
x2
3y?
3y?
2а0, + (у — а?)и, + (у + 2?)y — (у — а°) (2у — а?+
r3
Show that this system is hyperbolic with the characteristics
x2
V = y –
2
n =
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