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Unformatted text preview: ( 10 pts. ) u x + ( x + 1) u y = 0 [a] Sketch some characteristics. [b] Find the general solution. [c] Find the domain where exists the solution for the initial value problem: u ( x,x ) = sin( x ) , x ≥ 0. [d] What is special about the point x = 0 , y = 0 [e] Is the solution of this initial problem unique in the domain [c]? Justify your answer. Part 2. (Total 18 pts.) Problem: u x-2 xu y = 2 x y u, x > , y > [a] Sketch some characteristics. [b] Find the general solution. [c] Find the solution of the initial value problem: u (0 ,y ) = y 3 , 1 ≤ y ≤ 2. [d] Find and sketch the domain where the solution [c] exists and unique....
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This note was uploaded on 04/20/2011 for the course ENGINEERIN APM384 taught by Professor Chungonova during the Fall '11 term at University of Toronto.
- Fall '11