(a) Explanation Given information: Consider the autonomous differential equation d y d t = f ( y ) Calculation: From the graph you can see that the function has three zero (graph crosses y axis at threepoints) at y = − 2 , y = − 1 and y = 1 So, the differential equation has three solutions, one for each zero From the graph you can see that f ( y ) < 0 for y < − 2 , Ȁ (b) To determine To calculate: To sketch the graph of the solution that corresponds to the equation d y d t = f ( y ) that satisfies the initial conditions y(0)=0.

4th Edition

ISBN: 9781133383093

Author: Paul Blanchard; Robert L. Devaney; Glen R. Hall

Publisher: Cengage Learning US

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 1, Problem 41RE

(a)

To determine

To calculate:To sketch the slope field corresponds to the equation dydt=f(y)

(b)

To determine

To calculate:To sketch the graph of the solution that corresponds to the equation dydt=f(y) that satisfies the initial conditions y(0)=0.

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Chapter 1, Problem 40RE

Chapter 1, Problem 42RE

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Differential Equations

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To sketch the slope field corresponds to the equation d y d t = f ( y )

Solution Summary: The author illustrates how the slope field corresponds to the equation dyt=f(y).