Williams-Spring2010-Math108-M1-Problems

Williams-Spring2010-Math108-M1-Problems - ° = °?± and...

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Math 108 Williams Midterm 1 - 2/17/2010 60 Minutes; no notes, books, calculators; you may use the official formula sheets. Name: ______________________________________________________ Section 03 / Section 04 To receive credit, you must show your work, explain your reasoning, and demonstrate the use of the specific method indicated, when one is indicated. Clarity will be considered in grading. “I have adhered to the Duke Community Standard in completing this examination.” Signature: ___________________________________ 1. _____ 2. _____ 3. _____ 4. _____ 5. _____ Total (out of 24): ______
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1 1. (6 points) Find the general solution of ? ′′ + 4 ? = 3 ? 3 .
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2 2. A. (3 points) Find an integrating factor
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Unformatted text preview: ° = ° ?± and show that it transforms this equation into an exact equation (do not solve ): ² ? 2 + ? 2 ³?? − ?? ?? = 0 B. (2 points) Find a differential equation whose general solution is given by sin ? + ?± + ? 3 + ? 2 = ? 3 3. (5 points) Knowing that ? 1 = ? 2 is a solution to ? 2 ? ′′ − 2 ? = 0 , use the method of reduction of order to find a second solution to this equation. 4 4. (4 points) Show that the substitution ° = ?± + ?² + ? transforms the differential equation ?² ?± = ³ ( ?± + ?² + ? ) into a separable equation. 5 5. (4 points) Use the Laplace Transform to solve ? ′ = ° ( ± − ? ) ....
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This note was uploaded on 09/29/2010 for the course MATH 108 taught by Professor Trangenstein during the Spring '07 term at Duke.

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Williams-Spring2010-Math108-M1-Problems - ° = °?± and...

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