08SpringHwk05 - Math 3301 Reduction of Order Homework Set 5...

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Unformatted text preview: Math 3301 Reduction of Order Homework Set 5 10 Points 3 1. Find the general solution to 2 x 2 y - 3 x y - 3 y = 0 given that y1 ( x ) = x is a solution. You may assume that x > 0 for this problem. Fundamental Sets of Solutions 2. In the case of a complex root ( r1,2 = i ) I made the claim that the two solutions where y1 ( t ) = e t cos ( t ) and y2 ( t ) = e t sin ( t ) . Show that these two solution form a fundamental set t t of solutions and that the general solution in this case is y ( t ) = c1e cos ( t ) + c2e sin ( t ) . Clearly justify your answer. 3. Suppose that you know that f ( x ) = 1 1 x and W ( f , g ) = 4 sin . Determine the most general 2 x x 2 possible g ( x ) that will give this Wronskian. You may assume that x > 0 for this problem. Undetermined Coefficients, Part I For problems 4 7 use the method of undetermined coefficients to determine the general solution to the given differential equation. 4. 16 y - 24 y + 9 y = 25sin ( 6t ) 5. 4 y - 4 y + 5 y = 1 - 25t 3 6. y + 14 y + 24 y = 11e -5t 7. y + y - 2 y = -3t 2e -t 8. Solve the following IVP. y + 4 y = 6t cos ( 3t ) y ( 0 ) = 9, y ( 0 ) = 2 ...
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This note was uploaded on 05/22/2008 for the course MATH 3501 taught by Professor Smith during the Spring '08 term at A.T. Still University.

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