Matlab:

I'd like to apply y''+2y'+3y=e^(-2t) where y(0)=0, y'(0)=0 and y''-t^2*y'-2ty = 1 where y(0)=1, y'(0)=0 but how can we pass them for this program? since I don't fully understand f = @f(t,y)[0 1; -1 ....] here.

Please write @f(t,y) for them and appreciate if you explain how this function works.

I will thumb up if the solution seems corret, thank you :)

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function test()

a = 0;

b = 1;

%n = input('Enter the number of intervals:');

y = [2; -2];

t = 0:h:n*h;

% Define the function as an anonymous function

f = @(t,y) [0 1; -1 -exp(-3*t)]*y + [0; (5-2*exp(-3*t))*exp(-2*t)+1];

for i=1:n

k1 = f(t(i),y(:,i));

k2 = f(t(i)+0.5*h,y(:,i)+0.5*k1*h);

k3 = f(t(i)+h,y(:,i)-k1*h+2*k2*h);

y(:,i+1)= y(:,i)+h/6*(k1+4*k2+k3); %approximated value of the ODE using RK3

end

exact = exp(-2*t)+1;

disp(max(abs(exact-y(1,:))))

plot(t,y(1,:),'r',t,exact,'b--'),grid

xlabel('t'),ylabel('y')

legend('RK3','Exact')

end