dv/dt= f_in - f_out Here volume of water in the tank V is in litres, flow rate in f_in is in litres per hour, flow rate out f_out is in litres per hour and time t is in hours. Initially, the tank contains 50L of water: V (0) = 50. (a) Assume the rainfall throughout the day is getting heavier, such that, f_in(t) = 10 + t and that the tank is losing 10% of its volume of water per hour, such that, f_out (V) = 0.1V. Check by direct substitution that the function satisfies the ODE and initial condition V(t) = 10(t+5e^(-0.1t)) a has been solved b) assume home is slowly increasing, flow out rate increases with time: f_out(V,t)=0.1(1+0.1t)V solve the ODE for V(t) using either separation variables or integrating factor, include initial condition
change in volume
dv/dt= f_in - f_out
Here volume of water in the tank V is in litres, flow rate in f_in is in litres per hour, flow rate out f_out is
in litres per hour and time t is in hours. Initially, the tank contains 50L of water: V (0) = 50.
(a) Assume the rainfall throughout the day is getting heavier, such that, f_in(t) = 10 + t and
that the tank is losing 10% of its volume of water per hour, such that, f_out (V) = 0.1V. Check by direct substitution that the function satisfies the ODE and initial condition
V(t) = 10(t+5e^(-0.1t))
a has been solved
b) assume home is slowly increasing, flow out rate increases with time:
f_out(V,t)=0.1(1+0.1t)V
solve the ODE for V(t) using either separation variables or integrating factor, include initial condition
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