Exam 3 - The general solution (25 Marks)Find the general...

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Next: About this document MATH 1014.03MW Exam 4 Monday, March, 27 2000 NAME: Student Number: No. Marks Instructions : This exam contains 4 questions and has a total of 100 marks. Show all of your work. Time: 35 minutes. (20 Marks) Solve the following equation Solution (Method 1) Rewrite the equation as Integrating the above equation from 0 to t , we have and This implies . (Method 2) The general solution of the equation is Since s(0)=1000, we have C =1000. Hence, the required solution is (20 Marks)Find the general solution of the equation Solution Rewrite the equation as
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The integrating factor
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Unformatted text preview: The general solution (25 Marks)Find the general solution of the following equation. Solution (1) Find the general solution of y ''+6 y '+9 y =0. The auxiliary equation is . Solving the equation, we have r =-3. The general solution (2) [Note that and are particular solutions of y ''+6 y +9 y =0] Let . Then This implies 2 C =1 and C =1/2. Hence, (3) The required general solution is (25 Marks)Let and . Prove that Solution Taking the partial derivatives of , we obtain This implies and . Since and we obtain About this document . .. Kunquan Lan Mon Mar 27 10:04:47 EST 2000...
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Exam 3 - The general solution (25 Marks)Find the general...

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