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Unformatted text preview: 1 AMS 361: Applied Calculus IV by Prof. Y. Deng Quiz 1 Wednesday (03/09/2011) 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 Q1-1 Q1-2 Q1-3 Total Score Q1-1 (5 points): It is obvious that = satisfies the following DE. With this info, find its general solution = [ ( ) + + ]( − ) where ( ) is a given well-behaved function and “ a ” is a given constant. Solution: Substition: = + 1 We get = − 1 2 Substitute to the original DE, we get + ( ( ) + 2 ) + 1 = 0 Which is a 1 st order linear DE and solvable with the integrating factor method: 2 ( ) = exp ¡ ( ( ) + 2 ) ¢ Apply the integrating factor to the both sides of the...
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This note was uploaded on 05/09/2011 for the course AMS 361 taught by Professor Staff during the Spring '08 term at SUNY Stony Brook.
- Spring '08