# Solving simultaneous set of differential equations for range of values to get desired set output

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Josh on 20 Apr 2023
Answered: Davide Masiello on 20 Apr 2023
dXdt = (mu*X) - ((Fi/VL)*X);
dCdt = (mu*X*Ycx) - ((Fi/VL)*C);
dSdt = ((Fi/VL)*(S_in-S)) - (mu*X)/Yxs;
dProductdt = (mu*X*Ypx) - ((Fi/VL)*Product);
dVLdt = Fi;
I have solved these simultaneous differentials using ode15s in order to display their changes with time graphically for a set time period. Values such as S_in, Fi, mu and Ycx are inputted by myself from an allowable range. I am trying to get my outputs (X, C, S, Product and VL) within a certain (given) range by the end of this time span through iteration but its extremely tedious and quite unproductive. Is there a solver function that would iterate a certain range of values for input parameters until output parameters fell within a given range for this system?

Davide Masiello on 20 Apr 2023
I'd recommend taking a look at the material at the following link

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