SAMPLE_MATH12222_T109 - TERM 1 SAMPLE EXAMINATION 2009...

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TERM 1 SAMPLE EXAMINATION 2009 ENGINEERING MATHEMATICAL APPLICATIONS – MATH12222 Page 1 of 3 INSTRUCTIONS SHEET 1. Each question is worth 25 marks. 2. Students may attempt as many questions as they wish. It is expected that full marks can be obtained upon successful completion of four (4) questions. 3. Full working must be shown to obtain maximum credit. 4. All answers must be written in the Examination Answer Booklet provided.
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TERM 1 SAMPLE EXAMINATION 2009 ENGINEERING MATHEMATICAL APPLICATIONS – MATH12222 Question 1 25 Marks (a) Determine if each of the following differential equations is exact. If it is not exact find an integrating factor that will make it exact. Solve each equation using the provided initial condition: (i) ; 22 (2 2 2) 2 3) 0, (1) 2 xy y dx x y x dy y ++ + +− = = (ii) ) 1 = . 2 20 , ( 1 xy dx x y dy y += (10 marks) (b) Solve this differential equation 32 1 4, ( 1 ) 2 y xy ′ + x == (7 marks) (c) Solve the differential equation () 6 () 9 () yt y ft ′′ with initial conditions (0) 3 y = and (0) 1 y = in the cases: (i) () 0 ; ft = (ii) 3 () 72 t f te = .
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This note was uploaded on 04/29/2011 for the course ENGINEERIN MATH12222 taught by Professor Allanhancock during the Spring '09 term at Allan Hancock College.

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SAMPLE_MATH12222_T109 - TERM 1 SAMPLE EXAMINATION 2009...

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