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**Unformatted text preview: **Math 425 Dr. DeTurck Midterm 1 March 2, 2010 There are four problems on this test. You may use your book and your notes during this exam. Do as much of it as you can during the class period, and turn your work in at the end. But take the sheet with the problems home with you, and you may (re)work any problems you like and turn them in on Thursday for additional credit. 1. Solve u x- yu y + 2 u = 1, u ( x, 1) = 0. In what domain in the plane is your solution determined by the equation (even though the formula you get for u might define a valid function beyond this region)? 2. Find the general solution u ( x,y ) of the equation 3 u x + u xy = 1. 3. Let u ( x,t ) be the temperature in a rod of length L that satisfies the partial differential equation: u t = ku xx- ru for ( x,t ) (0 ,L ) (0 , ) , where k and r are positive constants this is related to the heat equation, but assumes that heat radiates out into the air along the rod together with the initial condition u ( x,...

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