9 solve the initial value problem 3 y 2 ux on the

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Unformatted text preview: itial condition u(x, 0) = cos x. 9. Solve the initial value problem 3 y 2 ux on the domain x 2xuy = x, u(0, y ) = y 2 0. Hint: In the course notes it is suggested that we should let ⇠ = x, and follow a standard procedure to find an appropriate expression for ⌘ . In this problem it’s much easier to reverse this; let ⌘ = y , and use the more complicated expression for ⇠ . BONUS: If the domain were given instead as y 0, and the initial condition were given as u (x, 0) = f (x), we would not necessarily be able to solve the problem (consider, for example, trying to solve this with u (x, 0) = x). Explain why. Are there any functions f (x) for which a solution would exist?...
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