Warning: Unable to find explicit solution.

I was trying to use dsolve for a system of ODE's (line 19 is the dsolve function)

1. d(Ca)/d(t)=-(k*ca*cb)-(vo*ca)/(Vo+vo*t)
2. d(Cb)/d(t)=-(k*ca*cb)+(vo(cbo-cb))/(Vo+vo*t)
3. d(Cc)/d(t)=(k*ca*cb)-(vo*cc)/(Vo+vo*t)
4. d(Cd)/d(t)=(k*ca*cb)-(vo*cd)/(Vo+vo*t)

k=2.2;
vo=0.05;
cbo=0.025;
Vo=5;
cao=0.05;
tspam=0:100:500;
syms cb(t) ca(t) cc(t) cd(t)
s=dsolve(diff(ca)==-(k*ca*cb)-(vo*ca)/(Vo+vo*t),diff(cb)==-(k*ca*cb)+(vo*(cbo-cb))/(Vo+vo*t),diff(cc)==(k*ca*cb)-(vo*cc)/(Vo+vo*t),diff(cd)==(k*ca*cb)-(vo*cd)/(Vo+vo*t),cc(0)==0,cd(0)==0,ca(0)==cao,cb(0)==cbo);



Warning: Unable to find explicit solution. 
> In dsolve (line 201)
  In Ejercicio4_29 (line 19) 

Answer 1

[madhan ravi]

dsolve() is not able to solve the problem so use ode45() instead:

k=2.2;
vo=0.05;
cbo=0.025;
Vo=5;
cao=0.05;
% tspam=0:100:500; %%?
syms cb(t) ca(t) cc(t) cd(t)
eq1 = diff(ca)==-(k*ca*cb)-(vo*ca)/(Vo+vo*t);
eq2 = diff(cb)==-(k*ca*cb)+(vo*(cbo-cb))/(Vo+vo*t);
eq3 = diff(cc)==(k*ca*cb)-(vo*cc)/(Vo+vo*t);
eq4 = diff(cd)==(k*ca*cb)-(vo*cd)/(Vo+vo*t);
vars = [cb(t); ca(t); cc(t); cd(t)];
V = odeToVectorField([eq1,eq2,eq3,eq4])
M = matlabFunction(V,'vars', {'t','Y'})
interval = [0 1.5];  %time interval
y0 = [cao cbo 0 0];      %initial conditions
ySol = ode45(M,interval,y0);
tValues = linspace(interval(1),interval(2),1000);
yValues = deval(ySol,tValues,1); %number 1 denotes first solution likewise you can mention 2 , 3 & 4 for the next two solutions
plot(tValues,yValues)

[Gabriela Tezanos Pinto]

First: Thank you so much for giving me a little or your time!!

it works for the first value but for the other it doesn`t. It`s supossed to be like the figure down here

[madhan ravi]

Upload your equations in latex form and the initial conditions.

[Gabriela Tezanos Pinto]

I'm sorry I don't understand, how do i change them to that latex form?.