3.1 Modeling with Differential Equations: Quiz


Problem 5

Consider the following differential equation:

y′ = −3y/x

Which of the follow graphs shows a possible solution curve? Explain your answers.


Answers, problem 5

Since y′ = −3y/x, the solution curve (where it appears) should be decreasing in quadrants I and III, and increasing in quadrants II and IV. Therefore graphs 3 and 4 are not possible solutions. Graph 1 happens to show the curve y = x−3 and graph 2 shows 1.5x−2, both of which satisfy the differential equation.


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