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Quiz-2-s11-Solution

# Quiz-2-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 2 Wednesday (03/30/2011) at 3:50PM-5:10PM in 137 Harriman (1) Closed Book with 1-page (double-sided 8.5x11) 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. (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: Problems To Grade? Score Remarks Q2-1 Q2-2 Q2-3 Total Score Q2-1 (5 points): For a given variable coefficient homogeneous DE, ! ! ! ! ! ! + ! ! !" !" + ! ! ! = ! one solution is given as ! ! ! ! . Find the general solution of this DE by finding another linearly indepdent solution ! ! ! = ! ! ! ! ! . Please note that ! ! ! , ! ! and ! ! are given functions while ! ! is not. Solution: First we must take all necessary derivatives of ! ! ! , ! ! ! ( ! ) = ! ! ! ! + ! ! ! ! ! !! ( ! ) = ! ! ! !! + ! ! ! ! ! + ! ′′ ! ! Plugging these values into the original DE, we obtain:

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Quiz-2-s11-Solution - AMS 361 Applied Calculus IV by Prof Y...

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