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NDSolve with side conditions:


The following ordinary differential equation system is given:
y'(t)=f1[y(t),x(t),z(t)]; x'(t)=f2[y(t),x(t),z(t)] and
z(t)=f3[y(t),x(t)]. z(t) is given in implicite and integrated form.

The question reads as follows: Can Mathematica solve this system
numerically by NDSolve. I have tried the following syntax:
NDSolve[{y'[t]==f1[y[t], x[t], z[t]], x'[t]==f2[y[t], x[t], z[t]],
z(t)==f3[y[t], x[t]], y[0]==y0, x[0]==x0, z[0]==z0},{y[t], x[t],
z[t]},{t, 0, 100}].

I could differentiate z(t)=f3[y(t),x(t)] with respect to t; this would
yield  a standard 3-dimensional DES. But I would like not to increase
the dimension.

Thanks for any help!


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