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Quiz3-s11-Solution

# Quiz3-s11-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 (04/27/2011) at 3:50-5:10PM in 137 Harriman (1) Closed book test with 1-page (double-sided 8.5x11) formulas (2) Do any two of the three problems. If all three are attempted, the two (and only two) best will be graded (3) Each problem is worth 5 points (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. SB ID Class ID Name NO NAME NO GRADES Problems Score Remarks Q2-1 Q2-2 Q2-3 Total Score Q3-1 (5 Points): Find the general solution for ! ! ! !!! + 4 ! ! ! !! + ! ! ! ! = 1 + ! + ! ! ! > 0 Solution: First, we introduce a new variable ! with the expression ! = !"# . Then ! = ! ! . We convert those nonlinear terms as some linear ones: ! ! ! = ! ! ! ! !! = ! ! ! ! ! !!! = 2 ! 3 ! + ! where ! , ! , ! are 1 st , 2 nd and 3 rd order derivative of y with respective to t, respectively. Then the original ODE is converted into the following form: ! + ! ! ! = 1 + ! ! + ! ! ! We come into solving a new constant-coefficient non-homogeneous O.D.E.

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