im having trouble finding the right values for this codes

% A 1500 gallon tank initially contains 600 gallons of water with 5 lbs of salt dissolved in it. 
% Water enters the tank at a rate of 9 gal/hr and the water entering the tank has a salt concentration 
% of 1/5*(1+cos(t)) lbs/gal. If a well mixed solution leaves the tank at a rate of 6 gal/hr, how much salt is in the 
% tank when it overflows?

%Setup the variables t and X(t) as the function of Salt in the tank over a period of time t.  
%Find also the derivative of X(t) and set as dX
syms t X(t)
dX = diff(X,t)

%Initial Conditions
Vo = 600
Vmax = 1500
cond1 = X(0)==5

%Flow Rates
cin = (1/5)*(1+cos(t))
qin = 9
qo = 6
V(t) = symfun(600+3*t,t)
co = X(t)/V

%Set the differential equation model as eqn1;
eqn1 = dX+((2*X)/(200+t))==((9/5)*(1+cos(t)))

%Find Xsoln  by solving the initial value problem eqn1 using cond1 
Xsoln = dsolve(eqn1,cond1)
x = solve(eqn1);
%Find the time when the tank will be full (tfull), that is when will the Volume reach Vmax
tfull = sym(300)

%Use the subs command to substitute t=tfull in the modelled equation. Save answer as XFull
XFull = subs(tfull,300)

% Plot the equation: Use the Title=Mixture of Salt Water, XValue=Time (in Hours), YValue=Amount of Salt (lbs)
Title = "Mixture of Salt Water"
XValue = "Time (in Hours)"
YValue = "Amount of Salt (lbs)"

%Use the domain (0, tfull+5) with 0.2 gaps from each point
x=0:0.1:tfull+5;
y=subs(Xsoln,t,x)
plot(x,y,'b--');
hold on;
title(Title);
xlabel(XValue);
ylabel(YValue);
plot(0,subs(Xsoln,t,0),'r*');
plot(tfull,subs(Xsoln,t,0),'r*');
hold off;

% Plot the equation: Use the Title=Mixture of Salt Water, XValue=Time (in Hours), YValue=Amount of Salt (lbs)

[Christella Bañaga]

it says that eqn1 and XFull has incorrect values

Answer 1

[Alan Stevens]

This should allow you to find the right values, though it might not be quite the way you were tasked to do it!

%Initial Conditions
V0 = 600; % gal
Vmax = 1500; % gal
X0 = 5; % lbs salt

tfull = (Vmax - V0)/3; % hrs
tspan = [0 tfull];

[t, X] = ode45(@fn, tspan, X0);

disp(['Amount of salt in tank when it overflows = ' num2str(X(end)) ' lbs'])

Amount of salt in tank when it overflows = 276.2121 lbs

% Plot the equation
Title = "Mixture of Salt Water";
XValue = "Time (in Hours)";
YValue = "Amount of Salt (lbs)";

plot(t,X,'b'), grid
title(Title);
xlabel(XValue);
ylabel(YValue);

% Amount of salt function
function dXdt = fn(t, X)
       
        V = 600 + 3*t;  % gal  
        dVindt = 9;  % gal/hr
        dVoutdt = 6; % gal/hr
        dXindt  = dVindt*(1/5)*(1 + cos(t));   % lbs/hr
        dXoutdt = dVoutdt*X/V;  % lbs/hr
        dXdt = dXindt - dXoutdt;  % lbs/hr
end

[Christella Bañaga]

it does not work :<

[Alan Stevens]

In what sense do you think it doesn't work?

Clearly the program works, though I used Matlab's in-built ode45 solver to do it, rather than the method you seem to have been asked to use. This should enable you to check if your result is close to the ode45 result.

[Christella Bañaga]

the program you provided works but not on the codes that im dealing with so that's why it does not work