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MATH 598 San Diego State University Math Equations Questions

MATH 598 San Diego State University Math Equations Questions

Question Description

7. For the first slope field for dL dt = 0.5(1 L) on the following page, (a) Using Jerry’s approach, sketch as accurately as possible a graph of the solution with initial condition L(0) = 1/3. (b) Make a copy of this sketch on a transparency. (c) If you wanted to obtain the graph of the solution with initial condition L(0) = 1/2, how, if at all, might you move the copy of your graph with initial value 1/3 so that it is now a graph of the solution with initial value 1/2? What feature of the di?erential equation justifies your approach? (d) Find the general solution for dL dt = 0.5(1 L) and explain how your results from part 7c can be understood from the general solution. 8. For the second slope field for dh dt = t + 1 on the following page, (a) Using Jerry’s approach, sketch as accurately as possible a graph of the solution with initial condition h(0) = 1/2. (b) Make a copy of this sketch on a transparency. (c) If you wanted to obtain the graph of the solution with initial condition h(0) = 1, how, if at all, might you move the copy of your graph with initial value 1/2 so that it is now a graph of the solution with initial value 1? Explain your idea and provide reasons for why your idea makes sense. (d) Find the general solution for dh dt = t + 1 and explain how your results from part 8c can be understood from the general solution. 9. Give an example of a di?erential equation where neither of your ideas from 7c and 8c will work and provide reasons for your response. Page 3.6 Unit 3: An Analytic Approach Slope Field for dL dt = 0.5(1 L) Slope Field for dh dt = t + 1 Page 3.7 Unit 3: An Analytic Approach


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