question_answer Q: Using this information, solve for the delay differential equation 3 x' (t) = 6 – x (t – to), (0.1)…A: Click to see the answer


Whilst solving the mixing problem:
Consider a large tank holding 1000 L of pure water into which a brine solution of salt begins
to flow at a constant rate of 6 L/min. The solution inside the tank is kept well stirred and is
flowing out of the tank at a rate of 6 L/min. If the concentration of salt in the brine entering the
tank is 0.1 kg/L, determine when the concentration of salt in the tank will reach 0.05 kg/L (see
Figure 3.2).
We encounter the initial value problem
x(1)
(6 L/min)
kg/L
1000
Зx (1)
kg/min .
500
(3)
0. Substituting the rates in (2)
The tank initially contained pure water, so we set x(0)
and (3) into equation (1) then gives the initial value problem
3x
0. -
dx
(4)
x(0) = 0,
dt
500
as a mathematical model for the mixing problem.
expand button
Transcribed Image Text:Whilst solving the mixing problem:
Consider a large tank holding 1000 L of pure water into which a brine solution of salt begins
to flow at a constant rate of 6 L/min. The solution inside the tank is kept well stirred and is
flowing out of the tank at a rate of 6 L/min. If the concentration of salt in the brine entering the
tank is 0.1 kg/L, determine when the concentration of salt in the tank will reach 0.05 kg/L (see
Figure 3.2).
We encounter the initial value problem
x(1)
(6 L/min)
kg/L
1000
Зx (1)
kg/min .
500
(3)
0. Substituting the rates in (2)
The tank initially contained pure water, so we set x(0)
and (3) into equation (1) then gives the initial value problem
3x
0. –
dx
(4)
x(0) = 0,
dt
500
as a mathematical model for the mixing problem.
Using this information, solve for the delay differential equation
3
x' (t) = 6 –
x (t – to) ,
500
(0.1)
x(t) = 0 for E [-to, 0] ,
(c) Use the method of steps to compute the solution to the initial value problem given
in (0.1) on the interval 0 < t < 15 for to = 3.
expand button
Transcribed Image Text:Using this information, solve for the delay differential equation
3
x’ (t) = 6 –
x (t – to) ,
500
(0.1)
x(t) = 0 for E [-to, 0] ,
(c) Use the method of steps to compute the solution to the initial value problem given
in (0.1) on the interval 0 < t < 15 for to = 3.
question_answer Q: Using this information, solve for the delay differential equation 3 x' (t) = 6 – x (t – to), (0.1)…A: Click to see the answer


Whilst solving the mixing problem:
Consider a large tank holding 1000 L of pure water into which a brine solution of salt begins
to flow at a constant rate of 6 L/min. The solution inside the tank is kept well stirred and is
flowing out of the tank at a rate of 6 L/min. If the concentration of salt in the brine entering the
tank is 0.1 kg/L, determine when the concentration of salt in the tank will reach 0.05 kg/L (see
Figure 3.2).
We encounter the initial value problem
x(1)
(6 L/min)
kg/L
1000
Зx (1)
kg/min .
500
(3)
0. Substituting the rates in (2)
The tank initially contained pure water, so we set x(0)
and (3) into equation (1) then gives the initial value problem
3x
0. -
dx
(4)
x(0) = 0,
dt
500
as a mathematical model for the mixing problem.
expand button
Transcribed Image Text:Whilst solving the mixing problem:
Consider a large tank holding 1000 L of pure water into which a brine solution of salt begins
to flow at a constant rate of 6 L/min. The solution inside the tank is kept well stirred and is
flowing out of the tank at a rate of 6 L/min. If the concentration of salt in the brine entering the
tank is 0.1 kg/L, determine when the concentration of salt in the tank will reach 0.05 kg/L (see
Figure 3.2).
We encounter the initial value problem
x(1)
(6 L/min)
kg/L
1000
Зx (1)
kg/min .
500
(3)
0. Substituting the rates in (2)
The tank initially contained pure water, so we set x(0)
and (3) into equation (1) then gives the initial value problem
3x
0. –
dx
(4)
x(0) = 0,
dt
500
as a mathematical model for the mixing problem.
Using this information, solve for the delay differential equation
3
x' (t) = 6 –
x (t – to) ,
500
(0.1)
x(t) = 0 for E [-to, 0] ,
(c) Use the method of steps to compute the solution to the initial value problem given
in (0.1) on the interval 0 < t < 15 for to = 3.
expand button
Transcribed Image Text:Using this information, solve for the delay differential equation
3
x’ (t) = 6 –
x (t – to) ,
500
(0.1)
x(t) = 0 for E [-to, 0] ,
(c) Use the method of steps to compute the solution to the initial value problem given
in (0.1) on the interval 0 < t < 15 for to = 3.

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