Practice_MT_2_Math_33B_W09

Practice_MT_2_Math_33B_W09 - Mathematics 33B - Practice...

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Unformatted text preview: Mathematics 33B - Practice Midterm 2 Instructor : D. E. Weisbart NAME (please print legibly): Your University ID Number: Your Discussion Section and TA: Signature: There are FOUR questions on this examination. This is an exam that I previously administered. Calculators, notes and books may not be used in this examination. The actual exam will be given on Friday, February 27th 2009 at 11:00am in Dodd 147. QUESTION VALUE SCORE 1 25 2 25 3 25 4 25 TOTAL 100 1 1. (25 points) a) Find the general solution of the equation y 00 + y- 2 y = 0. b) Find the general solution of the equation y 00 + y- 2 y = sin 3 t . Make sure to show your work. 2 c) Solve the equation b) with initial conditions y (0) = 0 and y (0) = 0. 3 2. (25 points) a) Find the general solution of the equation y 00- 4 y + 4 y = 0. b) Find the general solution of the equation y 00- 4 y + 4 y = e 2 t . 4 3. (25 points) Let y ( t ) and z ( t ) be solutions of the differential equation x 00 + ax + bx = 0. The Wronskian w ( y,z )( t ) of y ( t ) and z ( t ) is a function of t and w ( y,z )( t ) = y ( t ) z ( t )- y ( t ) z ( t ). Show that the Wronskian of y and z is either never zero or identically equal to 0. Hint: You should try to find a differential equation that the Wronskian satisfies and0....
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This note was uploaded on 03/17/2009 for the course MATH 33 taught by Professor Weisbart during the Winter '09 term at UCLA.

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Practice_MT_2_Math_33B_W09 - Mathematics 33B - Practice...

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