Explanation Given information: The given differential equation is y ′ = y 2 − 2 y + 1 with the initial condition y ( 0 ) = − 1 . Graph: The graph of the function g ( y ) = y 2 − 2 y + 1 on the y z coordinate system is shown in the following figure (a): The zero of the graph g ( y ) = y 2 − 2 y + 1 is at y = 1 . By using the property of differential equations: Corresponding to each zero of g ( y ) , there is a constant solution of the differential equation. Specifically, if g ( c ) = 0 , the constant function y = c is a solution. Thus, the differential equation y ′ = y 2 − 2 y + 1 has a constant solution at y = 1 . The graph (b) shows the constant solution on t y - coordinate system as shown below: To sketch of the solution, satisfying y ( 0 ) = − 1 , locate the initial value of y on the horizontal y - axis in graph (a) and vertical y - axis in graph (b).

15th Edition

ISBN: 9780137590612

Author: Goldstein

Publisher: RENT PEARS

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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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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 10, Problem 18RE

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To graph: The solutions of the differential equation y′=y2−2y+1 with initial condition

y(0)=−1 and indicates the constant solution

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Chapter 10, Problem 17RE

Chapter 10, Problem 19RE

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To graph: The solutions of the differential equation y ′ = y 2 − 2 y + 1 with initial condition y ( 0 ) = − 1 and indicates the constant solution

Solution Summary: The graph shows the constant solution of the differential equation yprime, which is shown in the following figure.

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To graph: The solutions of the differential equation y′=y2−2y+1 with initial condition

y(0)=−1 and indicates the constant solution

Want to see the full answer?

Chapter 10 Solutions

To graph: The solutions of the differential equation y ′ = y 2 − 2 y + 1 with initial condition y ( 0 ) = − 1 and indicates the constant solution

Solution Summary: The graph shows the constant solution of the differential equation yprime, which is shown in the following figure.

Concept explainers

Videos

To graph: The solutions of the differential equation y′=y2−2y+1 with initial condition y(0)=−1 and indicates the constant solution

Want to see the full answer?

Chapter 10 Solutions

To graph: The solutions of the differential equation y′=y2−2y+1 with initial condition

y(0)=−1 and indicates the constant solution