Question

Lab 6 Direction Fields Math 1B II. Some of the qualitative information that you derived above can be found without plotting a direction field. Some information can be observed in the differential equation y'=f(x,y). 5) Consider the differential equation y' = f(x,y), where f(x,y) is continuous and f(x, 3) = -1 for all x. If y(0) <3, can y(x) → as x increases? Explain your answer. (Hint: it may help to sketch what little you can of the direction field.) 6) Suppose y = 2 is a constant solution to the differential equation y' = f(x,y). a) What does this tell you about f(x,y)? b) What does this tell you about the slope field? c) What does this tell you about solutions with the initial y(0) + 2?

Answer 1

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