Question

For differential equations with water leaking out of the tank, is t defined including t = 0 and t = (final value) and why? Or do we just not include them?

Answer 1

tutorial.math.lamar.edu/Classes/DE/Modeling.aspx

Answer 2

Maybe t is defined at 0 and the final value for the solution of the equation, but that would be for the differential equation in the form: dx/dt =.... right?

Answer 3

yes, generaly they will tell you some value for the IVP like concentration = .30 and the tank is 100 gallons thus f(0) = 30 where f is the general solution

Answer 4

what do you mean by defined?
if the water level ‘W’ is a function of time ‘t’... then t is the independent variable.
yes, the domain of W(t) is limited from t=0 to W(t)=0 ... but it can be anything in between...