pmidterm1

pmidterm1 - 3. (a) (10 points) Show that the following...

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Math 33b Midterm 1 Lecture 2 Fall 2007 Name: Section: Instructions: There are 6 problems. Make sure 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, 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. Question Points Score 1 20 2 20 3 20 4 20 5 10 6 10 Total: 100
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1. (20 points) Solve the initial value problem: t dy dt + (2 t 2 + 3 t 3 ) y = te - ( t 2 + t 3 ) , y (0) = 5
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2. (a) (10 points) Solve the initial value problem: dy dt = 2 t ( y - 1) 2 , y (0) = 0 (b) (10 points) Solve the initial value problem: dy dt = 2 t ( y - 1) 2 , y (0) = 1
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Unformatted text preview: 3. (a) (10 points) Show that the following equation is exact: 2 x + y 2 + 2 xy dy dx = 0 (b) (10 points) Find the explicit solution to the initial value problem: 2 x + y 2 + 2 xy dy dx = 0 , y (1) = 1 4. (20 points) Find an integrating factor for the following equation (you do not need to solve the equation): 4 x 2 y + 2 y 2 + (3 x 3 + 4 xy ) dy dx = 0 Hint: It is of the form ( x, y ) = xy a for some a . 5. (10 points) Solve the initial value problem: dy dx = sin( y )(2 y-4)( y 3-6 y 2 + 12 y-8) , y (1) = 2 6. (10 points) Find the equilibrium solutions for the following equation, and identify them as asymptotically stable or unstable. dy dt = y 2-5 y + 6 Extra Scratch Paper:...
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pmidterm1 - 3. (a) (10 points) Show that the following...

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