Chapter 7, Problem 37RE

To determine

To construct a slope field for the differential equation.

Answer to Problem 37RE

The required solution is,

  

Explanation of Solution

Given information: The equation is, $\frac{dy}{dx}=-x$

Graph,

  

Calculation: The required solution is obtained as,

Since, the differential equation has $x$ only, substitute each $x$ coordinate of the points in the graph. You will then use that slope as the slope of all the points with that $x$ coordinate.

  $\begin{array}{l}\frac{dy}{dx}=-x\\ x=-1:\frac{dy}{dx}=-\left(-1\right)=1\\ x=0:\frac{dy}{dx}=-\left(0\right)=0\\ x=1:\frac{dy}{dx}=-\left(1\right)=-1\end{array}$

At each point with an $x$ coordinate of -1, draw a line segment with a slope of 1. At each point with an $x$ coordinate of 0, draw a line segment with an slope of 0. At each point with an $x$ coordinate of 1, draw a line segment with a slope of -1.