Question: Equation concerning solutions of ODE system

Hello all,

I have an ODE system (please see bellow) where my unknowns are S(t) and K(t), all the the other symbols are known parameters. This system, by given the initial values for S and K, that is, S(0)=100 and K(0)=20, I can solve numerically.

sys:= diff(S(t), t) = -eta*K(t)*S(t)/(w*N*(S(t)+K(t))), diff(K(t), t) = eta*K(t)*S(t)/(w*N*(S(t)+K(t)))+S(t)*(-z*eta*alpha*K(t)^2+(-z*eta*alpha*S(t)-(eta*alpha^2*S(t)^2-2*N*C[max]*w*eta*alpha*K(t)+((-N*w+z)*alpha+N*C[max]^2*w*eta)*w*N)*upsilon)*K(t)+N*S(t)*w*alpha*upsilon*(N*w-z))/((K(t)^2*alpha*z+3*K(t)*S(t)*alpha*z+(2*S(t)*z*alpha+upsilon)*S(t))*w*N)

In addition, I have an algebraic equation:

eq1:= -c2 + (K(t2)*S(t2)+w*N*S(t2))*z=0,

where S(t2) and K(t2) are the solutions of my ODE sys in S and K at t=t2. The t2 is unknown time variable. 

My question is: how can I find t2 such that my algebraic equation (eq1) is satisfied.

Thanks in advance,

Dmitry