syms a b c d e f x real
syms y0 dy0 ddy0 y1 dy1 ddy1 real

g = a*x^5 + b*x^4 + c*x^3 + d*x^2 + e*x + f
dg = diff(g, x)
ddg = diff(dg, x)

g0 = subs(g, x, 0)
dg0 = subs(dg, x, 0)
ddg0 = subs(ddg, x, 0)

g1 = subs(g, x, 1)
dg1 = subs(dg, x, 1)
ddg1 = subs(ddg, x, 1)

S = solve( g0-y0, dg0-dy0, ddg0-ddy0, g1-y1, dg1-dy1, ddg1-ddy1, ...
a, b, c, d, e, f)