A large tank holds 1000 gallons of water containing 50 pounds of dissolved salt. Suppose a solution of salt water with a concentration of 0.02 pounds of salt per gallon of water flows into the tank at a rate of 5 gallons per minute. The solution in the tank is well stirred and flows out a hole in the bottom of the tank at the constant rate of 3 gallons per minute. Let x (t) be the amount in pounds of salt in the tank at time t, where x(0) = 50 pounds. The differential equation giving the rate of change x'(t) of salt measured in pounds per minute in the tank is 3x (t) x' (t) = 0.1 1000 + 2t Use Taylor's method of order 2 (by hand) with h = 1 (time step = 1 minute) to find the concentration of salt after two minutes.
A large tank holds 1000 gallons of water containing 50 pounds of dissolved salt. Suppose a solution of salt water with a concentration of 0.02 pounds of salt per gallon of water flows into the tank at a rate of 5 gallons per minute. The solution in the tank is well stirred and flows out a hole in the bottom of the tank at the constant rate of 3 gallons per minute. Let x (t) be the amount in pounds of salt in the tank at time t, where x(0) = 50 pounds. The differential equation giving the rate of change x'(t) of salt measured in pounds per minute in the tank is 3x (t) x' (t) = 0.1 1000 + 2t Use Taylor's method of order 2 (by hand) with h = 1 (time step = 1 minute) to find the concentration of salt after two minutes.
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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Transcribed Image Text:A large tank holds 1000 gallons of water containing 50 pounds of dissolved salt. Suppose a solution of
salt water with a concentration of 0.02 pounds of salt per gallon of water flows into the tank at a rate of
5 gallons per minute. The solution in the tank is well stirred and flows out a hole in the bottom of the
tank at the constant rate of 3 gallons per minute.
Let x (t) be the amount in pounds of salt in the tank at time t, where x(0) 50 pounds. The differential
equation giving the rate of change x'(t) of salt measured in pounds per minute in the tank is
x' (t) = 0.1 -
3x(t)
1000 + 2t
=
1 (time step = 1 minute) to find the concentration of
Use Taylor's method of order 2 (by hand) with h
salt after two minutes.
=
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