How can I manipulate variables in an NDSolve differential equation?

Questions
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1 
ecosh =
 NDSolve[{ex'[t] == r - (a*h*ex[t] ep[t]), 
    ep'[t] == (f*a*ex[t]*ep[t])/(1 + a*h*ex[t]) - q*ep[t], 
    ex[0] == 300, ep[0] == 100} /. {a -> 0.1, h -> 0.1, q -> 0.115, 
    f -> 0.15, r -> 0}, {ex, ep}, {t, 0, 50}]
Plot[Evaluate[{ex[t], ep[t]} /. ecosh], {t, 0, 10}]

ScreenShot2014-01-10at1.50.53AM.png
ScreenShot2014-01-10at1.50.53AM.png371×233 7.71 KB

That’s my code and there’s the plot it yields. I’m tweaking a model and I want to be able to adjust all the parameters (i.e. a, h, q, f, r) as well as the starting conditions (ex[0] and ep[0]) quickly. However I haven’t found a way that’s compatible with using NDSolve. Any ideas?

2

ParametricNDSolve gives you an NDSolve setup than contains parameters.

http://reference.wolfram.com/mathematica/ref/ParametricNDSolve.html

3

Hi,
I do these types of things all of the time. I typically take the Manipulate approach. In this approach, wrap the NDSolve function in a Manipulate, and give each parameter a range of values. Just think of this as using Table to specify lists for each of the parameters, then you could iteratively search through the list or specify different values.