DSolve fails with initial condition in the differential equation

[sirion]

Having some troubles getting further in this system I'm trying to solve. The notebook's at http://www.gabrielwyner.com/fluids5.nb

PDF form:
http://www.gabrielwyner.com/fluids5.pdf

I guess the most current problem involves mathematica complaining about DSolve[h'[t] = f[h[t],h[0]]] (with correct syntax, that is). It doesn't like solving a function with h[t] and h[0] in it..

 

[Hurkyl]

Try replacing h[0] with some arbitrary constant, k... then (at some point) imposing the initial condition that h[0] = k.

 

[sirion]

That works, but eventually I need to solve for the h[0] that maximizes another function of h[t]. Was hoping to get a function for h[t], plug it into u[t], plug that into v[t], plug *that* into k[t] and plot that vs h[0]. Am I going to run into trouble if h[0] isn't part of the original h[t] function?