problem with a differential algebraic equation system

Hello, i face problem trying to solve the following differential algebraic equation system:

d(x1)=f1(x1,t)

d(x2)=f2(x2,t)

d(x3)=f3(x3,t)

d(x4)=f4(x4,x5,t)

d(x5)=f5(x4,x5,x6,t,z)

d(x6)=f6(x5,x6,t)

g(x1,x2,x3,t)=0 =>x1(t)+x2(t)+x3(t)=C(constant value) (specifically this is the algebraic function g analytically)

h(x1,x2,x3,x4,x5,t,z)=0 (algebraic function h is more complicated, it includes log function also between the unknown variables)

If you could give me a method to solve it , i would be gratefull.

Till now i'm using numerical analysis to solve it (using ode23 function from matlab), but i do not know how to solve the differential equations in parallel with the algebraic ones.

Thank you in advance