plot (xy^3)/(1+y^2) = 8/5 2d graph in matlab

To plot the 2D graph for the equation (xy^3)/(1+y^2) = 8/5 in MATLAB, we first need to solve for y as a function of x in terms of the equation given.

xy^3 = (8/5)(1+y^2)

xy^3 = (8/5) + (8/5)y^2

y^2 = (5/8)(xy^3 - 8/5)

y = sqrt((5/8)(xy^3 - 8/5))

After obtaining the function for y in terms of x, we can now plot it using the plot function in MATLAB. We choose a range of x values to plot, and then evaluate y for each of these x values using the function we obtained earlier.

Here's the code to plot the graph:

main.m
% define the equation as a function of y in terms of x
y = @(x) sqrt((5/8) .* (x.*y(x).^3 - 8/5));

% choose a range of values for x
x_values = -10:0.1:10;

% evaluate y for each value in the range of x
y_values = y(x_values);

% plot the graph
plot(x_values, y_values);
grid on;
xlabel('x');
ylabel('y');
title('(xy^3)/(1+y^2) = 8/5');
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This will produce a 2D graph of the equation in MATLAB, with the x values ranging from -10 to 10 and a step size of 0.1. You can adjust the x range and step size as needed to obtain a clearer view of the graph.