Fifth Order Polynomial Approximation without using Polyfit

Hello Everyone

I want to find fifth-order polynomial approximation p(x) = 3/2 + c1*x1 + c2*x2 + c3*x3 + c4*x4 + c5*x5 with the initial value condition of Dy = x^2 + y^2, y(0) = 3/2.

The easiest way to do it is by using Polyfit function but if I want to not use internal function and derive the approximation by using ITERATION, how should I code it in Matlab? Say I want to utilize Taylor algorithm for it

Thank you

[darova]

Do you have data to fit ?