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.