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pmidterm2

# pmidterm2 - =-8 y(b(20 points Suppose y is a solution for...

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Math 33b Midterm 2 Lecture 2 Fall 2007 Name: Section: Instructions: There are 3 problems. Problems 1 and 2 each have two parts. Make sure that you are not missing any pages. Show all work in detail or your answer will not receive credit. Write neatly and box all answers. No calculators, PDA’s, cell-phones, books, or notes are allowed. Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. Do not use your own scratch paper. Extra scratch paper is available from the front of the room. If you have extra time, you might want to check your answers. Question Points Score 1 40 2 40 3 40 Total: 120

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1. (a) (20 points) Find the general solution for 2 y 00

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Unformatted text preview: =-8 y (b) (20 points) Suppose y is a solution for the initial value problem 2 y 00 =-8 y, y (0) =-2 , y (0) =-4 √ 3 Find t with-π ≤ t < π so that y ( t ) = 4 Hint: One way to ﬁnd t is by examining the graph of y. Hint: cos( a + b ) = cos( a ) cos( b )-sin( a ) sin( b ) . 2. (a) (20 points) Find the general solution for: y 00-2 y + y = 0 (b) (20 points) Find the general solution for: y 00-2 y + y = e t 3. (40 points) Without using the shortcut formula from the book, ﬁnd a solution for: ty 00-(1 + t ) y + y = t 2 e 2 t Hint: 1 + t and e t are each solutions for ty 00-(1 + t ) y + y = 0 Hint: R te t dt = te t-e t Extra Scratch Paper: Extra Scratch Paper:...
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pmidterm2 - =-8 y(b(20 points Suppose y is a solution for...

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