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Determining Constants in Differential Equations

Understand how to find C0 and C1 in differential equation solutions and the significance of including C2 in conjectures.

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Determining Constants in Differential Equations

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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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