Are you allowed to use existing code? So if you have the curve fitting toolbox, you can just use csape.
x = 0:4;
y = [1 3 3 4 2];
spl = csape(x,y,'variational')
struct with fields:
breaks: [0 1 2 3 4]
coefs: [4×4 double]
As you can see, the second derivative as plotted is zero at the ends, and the second derivative curve is piecewise linear. So csape did as was needed, producing a natural cubic spline interpolant.
Plotting the plsine is pretty easy too.
However, I would not be remotely surprised if your question is to actually formulate the equations and then solve for the spline yourself. After all, this is surely homework. So is that your need? (I'm not at all sure why you would be doing this for any other purpose than homework.)
If your need is to formulate the plsine completely from scratch, then my hope is you are not asking someone to do that part for you. It is easy enough to do anyway. Start by reading here: