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Using this information, solve for the delay differential equation 3 x'(t) = 6 – x (t – to), 500 (0.1) | x(t) = 0 for x € [-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

Using this information, solve for the delay differential equation 3 x'(t) = 6 – x (t – to), 500 (0.1) | x(t) = 0 for x € [-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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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.
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.
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.
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