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Quiz-2-s11 - another linearly indepdent solution = Please...

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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, ! ! ! ! ! ! + ! ! !" !" + ! ! ! = 0 one solution is given as ! ! ! 0 . Find the general solution of this DE by finding
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Unformatted text preview: another linearly indepdent solution ! ! ! = ! ! ! ! ! . Please note that ! ! ! , ! ! and ! ! are given functions while ! ! is not. Q2-2 (5 points): Find the general solution of the following DE: ! ! ! + 2 ! ! + ! = 5 ( sin ! + cos ! ) Q2-3 (5 points): If a projectile leaves Earth’s surface at velectiy ! ! , please derivate the formula for the later velocity as a function of the distance ! from the projectile to the center of the earth. The earth’s radius ! and gravitational constant ! are given ( 3 Points ). Also, naturally, the velocity has to be a real number. Compute the condition at which the velocity will become imaginary ( 2 Points )....
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