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Differential Equations and Slope Field Analysis

Explore differential equations, slope fields, and approximations using Euler's Method, with examples and true/false questions.

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Differential Equations and Slope Field Analysis

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  1. Class 4, #4: Which of the following DEs would generate the slope field below? • y’=yt • y’=y/t • y’=-yt • y’=-y/t

  2. Class 4, #5: Consider the slope field which shows the derivative y’ for a range of values for the function y and independent variable t. Suppose y(0)=-4. Predict y(5).

  3. Class 4, #6: Using Euler’s Method, we set up the difference equation yn+1=yn+cΔt to approximate a differential equation. What is the differential equation? • y’=cy • y’=y+c • y’=c • y’=y+cΔt • None of the above

  4. Class 4, #7: Consider the differential equation y’=ay+bwith parameters a and b.To approximate this differential equation using Euler’s Method, what is the difference equation?

  5. Class 4, #8: We have used Euler’s Method to approximate the solution to a differential equation with the difference equation zn+1=1.2zn. We know that the function z(0)=3. Estimate z(2).

  6. Class 5, #1: TRUE or FALSE: “All equations have solutions.” A. TRUE B. FALSE.

  7. Class 5, #2: TRUE or FALSE: “Some initial value problems do not have unique solutions.” A. TRUE B. FALSE.

  8. Class 5, #3: TRUE or FALSE: “IF an initial value problem has a solution, THEN it is unique.” A. TRUE B. FALSE.

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