Category:Installation: Difference between revisions

% Define the function dy/dx = yx - x^3 f = @(x, y) y*x - x^3;

% Initial conditions x0 = 0; y0 = 1; h = 0.6; xf = 1.8;

% Number of steps n = round((xf - x0) / h);

% Initialize arrays for solutions x_values = x0:h:xf;

% Euler's Explicit Method y_euler = zeros(1, n+1); y_euler(1) = y0; for i = 1:n

   y_euler(i+1) = y_euler(i) + h * f(x_values(i), y_euler(i));

end

% Display results disp('x values:'), disp(x_values); disp('Euler method results:'), disp(y_euler);

% Plot the solutions figure; plot(x_values, y_euler, '-o', 'DisplayName', 'Euler Method'); hold on; xlabel('x'); ylabel('y'); title('Solutions to dy/dx = yx - x^3'); legend; grid on;