) Sketch the directional field of the equation. (Preferably, using the isoclines you found in (a)).
Use 2, 1,-1,-2,0
Sketching directional field using MATLAB.
To sketch the directional field of the differential equation at the points using MATLAB, you can follow these steps:
Open MATLAB.
Define the differential equation .
Create a grid of points where
takes the values .Calculate the corresponding values using the differential equation.
Use the
quiverfunction to plot the directional field using the calculated and values.
Here's the MATLAB code to accomplish this:
% Define the differential equation
dydt = @(y) 1 - y;
% List of y values
yValues = [2, 1, -1, -2, 0];
% Create a grid of points
[y, yprime] = meshgrid(yValues, dydt(yValues));
% Calculate the corresponding y' values
yprime = dydt(y);
% Plot the directional field
quiver(y, yprime, ones(size(y)), yprime, 0.5, 'b');
hold on;
plot(yValues, dydt(yValues), 'ro', 'MarkerSize', 8);
xlabel('y');
ylabel("y'");
title("Directional Field of y' = 1 - y");
grid on;
hold off;
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