quiz1sol - 1 This is a second order PDE because of the u xx...

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TA: R McDougal Name: Math 415 27 September 2007 Quiz I Answer each question as completely as you can; remember you must show all work for full credit. You may not consult books, notes, or each other for this quiz. Good luck! Consider the differential equation u t = - x 2 2 u xx (1) 1. State the order of (1). (3 points) 2. State whether (1) is linear or nonlinear. (3 points) 3. Verify that u = x 2 e - t is a solution of (1). (4 points)
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Unformatted text preview: 1. This is a second order PDE because of the u xx term. 2. This equation is linear. (Note that x and t are independent variables, so the x 2 doesn’t matter.) 3. To verify this, we simply plug in and see if it works: LHS: u t =-x 2 e-t . RHS:-x 2 2 u xx = x 2 2 · 2 e-t =-x 2 e-t , so the LHS=RHS, so we have a solution....
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