find the (approximate) value of y(0.5) for dy/dt = t^2 + y^2, y(0)=1 on the interval [0, 0.5] in matlab

main.m
% Define the differential equation dy/dt = t^2 + y^2
dydt = @(t, y) t.^2 + y.^2;

% Define the initial condition
y0 = 1;

% Define the interval
tspan = [0 0.5];

% Solve the differential equation using ode45
[t, y] = ode45(dydt, tspan, y0);

% Interpolate the value of y at t=0.5
y_at_05 = interp1(t, y, 0.5);

% Display the result
disp(['The approximate value of y(0.5) is ', num2str(y_at_05)]);
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