How to numerically solve first order differential equation with dependent variables?

My equation looks like this:

(a1*b1*c1+a2*b2*c2)dT/dt = u*p*V(t) - (k1+k2)*(T-Tinf)

with an initial condition: T(0)=Tinf and V(t)=V0(1-t/ts)

I'm very new to matlab and have been trying to implement dsolve and ode45, but can't figure out how to include the initial condition and the velocity function within the solution. Any help is appreciated.

[James Tursa]

Please post the code you have tried so far and we can point you in the right direction.

[Michael Ortiz]

I tried this to start with, just to see what would happen and predictably I received many errors.

function Vel=fvel(t)
Vel=V0(1-t/ts);
function Tdot=ftemp(t,T)
Tdot=(u*p*vel(t)-(k1+k2)(T-25))/(a1*b1*c1+a2*b2*c2); %Tinf=25
 
>> t0=0; tf=ts; T0=25;
>> [t,T]=ode45('ftemp',[t0 tf],T0);

Answer 1

[darova]

You didn't declared variables inside each function

Do this like this

function Vel=fvel(t)
V0 = 5;
ts = 0.3;
Vel = V0*(1-t/ts);