%y(t+2) + y(t+1) - 2y(t) = 12, t>=0
%y(1) = 4, y(2) = 5
t=[1:30];
y(1) = 4;
y(2) = 5;
for m=3:30;
    y(m)=-y(m-1)+2*y(m-2)+12;
end
stem(t,y,'o')
stem(t,y)
pause;
plot(t,y,'*')
pause
plot(t,y)
pause;
f = @(new_y) interp1(t,y, new_y, 'spline');
x=[1:.1:30];
for i = 1:291
ff(i)=f(x(i));
end
for i = 1:291
yte(i)=3+(-2)^(x(i)-1)+4*(x(i)-1);
end
plot(x,ff,'r-',x,yte, 'b:')
xlabel ('tempo')
ylabel ('y')
title ('Curvas contínuas: spline (vermelha) e teórica (azul tracejado)')