MATH2065: Introduction to Partial Differential Equations Semester 2 2011 Assignment 1 This assignment is due by 4pm Thursday 1 September. It should be posted in the locked collection boxes at the eastern end of Carslaw Level 3. Your assignment with a cover sheet should be stapled to a manilla folder on the cover of which you should write the initial of your family name as a LARGE letter. Warning: these boxes are near room 350 and the pyramids. They are NOT the boxes used for the collection of rst year assignments at the western end of Carslaw level 3. 1. [5 marks] Find the general solution y(t) of the ordinary dierential equation y00 ?? !2y = e!t; where ! is a non-negative constant. (Consider the ! = 0 and ! > 0 cases sepa- rately). 2. [5 marks] Use Laplace transform to solve the following dierential equation for y(t): d2y dt2 ?? 4dy dt + 3y =8 1; given that y(0) = 0 and y0(0) = 2. 3. [5 marks] Consider the following partial dierential equation for u(x; t) @2 @x2 @2u @x2= @2u @t2 : (a) [2 marks] If is a function of t derive two ODEs by separation of variables. (Do not try to solve the separated equations.) (b) [3 marks] If is a function of x derive two ODEs by separation of variables. (Do not try to solve the separated equations.)
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