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Question: consider the problem uquot x u x f x...

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Consider the problem u (x) + u, (x) f (x) ,0 < x < 1 = with f a given function (a) Is there one and only one solution i.e is any solution necessarily unique? Explain. (Hint: Take the difference w of any two so- lutions and solve the resulting boundary value problem for the difference w to show that any solution u cannot be unique.) b) Does a solution necessarily exist or or is there a condition that f (x) must satisfy for existence of solution? Explain. (Hint: In- tegrate the ODE from 0 to and derive a condition which the function f must satisfy.)

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