Chapter 6.1, Problem 31E

To determine

To draw: The slope field of the graph of the given differential equation.

Answer to Problem 31E

The graph is:

  

Explanation of Solution

Given information:

The differential equation is: $\frac{dy}{dx}=2x+y$

And the graph is:

  

Calculation:

The given differential equation is: $\frac{dy}{dx}=2x+y$

Entrusted with performing a slope analysis on the twelve lattice points of the provided graph in order to set up a slope field.

Set up the table below to begin the analysis.

Table 1: Slope value at each point $(x,y)$

  

  $x$ and $y$ values should now be entered into the supplied differential equation.

Create line segments now that reflect the direction of the slopes at each point. now get the slope field for the given differential equation that is represented :

  

Therefore the required slope field of the graph of the given differential equation $\frac{dy}{dx}=2x+y$ .