Sure, here's a simplified Octave code example to solve a differential equation using Euler's method with different step sizes and plot the results. In this code, we'll use a simple example of a differential equation with an initial condition. Replace the `f(x, y)` function with your specific equation.

```octave
% Define the differential equation function f(x, y)
function dydx = f(x, y)
    % Define your specific differential equation here, for example: dydx = -0.1 * y
    dydx = -0.1 * y; % Example equation: y' = -0.1 * y
end

% Initial values
x0 = 0;
y0 = 1;

% Time interval
target_x = 480;

% Step sizes
step_sizes = [240, 120, 60, 10, 5];

% Initialize arrays to store results
x_values = cell(1, numel(step_sizes));
y_values = cell(1, numel(step_sizes));

% Loop through different step sizes
for i = 1:numel(step_sizes)
    x = x0;
    y = y0;
    h = step_sizes(i);
    x_result = [];
    y_result = [];

    while x < target_x
        slope = f(x, y);
        y = y + h * slope;
        x = x + h;
        x_result = [x_result; x];
        y_result = [y_result; y];
    end

    x_values{i} = x_result;
    y_values{i] = y_result;
end

% Plot the results
figure;

for i = 1:numel(step_sizes)
    plot(x_values{i}, y_values{i}, 'DisplayName', sprintf('h = %d', step_sizes(i)));
    hold on;
end

xlabel('Time (seconds)');
ylabel('Temperature');
title('Euler''s Method with Different Step Sizes');
legend('Location', 'best');
grid on;

hold off;
```

Make sure to replace the `f(x, y)` function with your specific differential equation. This code will help you solve the equation and plot the results for different step sizes.