Math Problem Set 4: Conjectures and Solutions

set 4 question 1 when we have y 7y 2x we should n.w

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Explore various mathematical problems involving conjectures, solutions, and differential equations. Includes identifying solutions, determining parameter values, and analyzing system behaviors. Get ready to delve into mathematical reasoning and problem-solving techniques.

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Uploaded on Apr 21, 2025 | 0 Views

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Set #4, Question 1: When we have y =7y+2x we should conjecture y=C0e7x+C1x+C2.Why include theC2?

Set #4, Question 2: We are testing the function f(x)=C0e2x+C1e-2x as a possible solution to a DE. After we substitute the function and its derivative into the DE we get 2C0e2x -2C1e-2x = -2(C0e2x+C1e- 2x)+3e2x. What value of C0 will allow this function to work as a solution?

Set #4, Question3: We are testing the function f(x)=C0e2x+C1e-2x as a possible solution to a DE. After we substitute the function and its derivative into the DE we get 2C0e2x -2C1e-2x = -2(C0e2x+C1e- 2x)+3e2x. What value of C1 will allow this function to work?