Quiz-3-s12-SOLUTION

# Quiz-3-s12-SOLUTION - AMS 361 Applied Calculus IV by Prof Y...

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1 AMS 361: Applied Calculus IV by Prof. Y. Deng Quiz 3 Wednesday (04/25/2012) at 5:20PM-6:40PM in 001 ESS (1) Closed Book with 1-page (double-sided 8.5x11) self-prepared formulas. (2) Do any two of the three problems. If all three are attempted, the two best (and only two) will be graded. (3) Each problem is worth 5 points for a total of 10 points (max). (4) No points for guessing work and for solutions without appropriate intermediate steps; Partial credits are given only for steps that are relevant to the solutions. (5) No name, no grade and no question asked or answered. SB ID Name Problems To Grade? Score Remarks Q2-1 Q2-2 Q2-3 Total Score Q3-­‐1 (5 Points): Find the general solution of the following non-­‐homogeneous DE using your favoriate method: ࠵? ! ࠵? !! + 2 ࠵? ! ࠵? ! 12 ࠵? ! ࠵? = 1 Solution : Method I (Undetermined Coefficients) This problem is a Cauchy-­‐Euler equation, so its solution should be a polynomial. To find the homogeneous solution, use the trial function ࠵? = ࠵? ! and plug into the homogeneous equation first ࠵? ! ࠵? ! !! + 2 ࠵? ! ࠵? ! ! 12 ࠵? ! ࠵? ! = ࠵? ࠵? 1 + 2 ࠵? 12 ࠵? ! ! ! = ࠵? ! + ࠵? 12 ࠵? ! ! ! = 0 ࠵? + 4 ࠵? 3 = 0 ࠵? = 4 ࠵?࠵? ࠵? = 3 Thus, ࠵?

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