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Question 4 : We have the equation y’=2y+sin(3t). What should our conjecture be?

Question 1 : We are testing the function f(x)=C 0 e 2x + C 1 e -2x as a possible solution to a DE. After we substitute the function and its derivative into the DE we get 2 C 0 e 2x -2 C 1 e -2x = -2( C 0 e 2x + C 1 e -2x )+3e 2x . What value of C 0 will allow this function to work?.

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Question 4 : We have the equation y’=2y+sin(3t). What should our conjecture be?

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  1. Question 1: 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?

  2. 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 C1 will allow this function to work?

  3. Question 3: When we have y’=7y+2x we should conjecture y=C0e7x+C1x+C2.Why include theC2?

  4. Question 4: We have the equation y’=2y+sin(3t). What should our conjecture be?

  5. Question 5: Consider g’(z)=ag+bcos(cz) where a, b and c are positive parameters. What will the long-term behavior of the system be?

  6. Question 6: Which of the following is NOT a solution to y’(t)=5y+3t?

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