Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped at a slower rate of 2 gal/min. If the concentration of the solution entering is 2 lb/gal, determine a differential equation for the amount of salt A(t) in the tank at time t.

Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped at a slower rate of 2 gal/min. If the concentration of the solution entering is 2 lb/gal, determine a differential equation for the amount of salt A(t) in the tank at time t.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: a. Classify and solve the first order differential equation y' = /2 +e'.

A: Answer Linear differential equation is of the form y'+Py=Q Where P,Q are function of t.

Q: The growth of a new restaurant depends on the number of its regular customers as p'(t) = .05√p(t)…

A: TA differential equation is a equation that connects the derivatives of one or more unknown…

Q: Find the general solution to the separable differential equation: (2x + 1)(x + 1)y' = - %3D For full…

Q: When a capacitor of capacity C is being charged through a resistance R by a battery which supplies a…

A: Given: RdQdt + QC=E The given equation can be written as dQdt +QC=ER

Q: In the given question , determine whether the function is a solution of the differential equation…

A: Substitute the value of y in the equation to determine whether the function is a solution to it or…

Q: Find the general solution of the first order differential equation (x+2) y′ + 4y = (3x + 6)-2 lnx.

A: Given: x+2y'+4y=3x+6-2lnx for finding solution of given differential equation, first we convert it…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A: Given, In a certain company, the relationship between the price per unit P and the weekly sale y,…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

Q: Consider the following model for a population that is changing due to births, deaths, immigration,…

Q: determine the general solution to thegiven differential equation. y′′′ − y′′ + y′ − y = 0.

Q: A murder of crows in the wild is observed to double its population in one year. However, in…

Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

A: Explanation we have given the voltage change E across the heart satisfies the linear differential…

Q: What is the general solution to the the differential equation3y"'-y' - 2y=0?

Q: Find the general solution of the first-order linear differential equation y′ − y = 10

Q: Solve for the General Solution of the given Differential Equation y' = y – xy³e- -2x

Q: What is the solution of the first order differential equation y(k + 1) = y(k) + 5.

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

Q: Suppose you have the differential equation: y' + p(x)y ln(y) = q(x)y. Prove that the substitution v…

Q: Suppose the auxiliary equation of a homogeneous linear differential equation has roots m_1=-2 and…

A: We have given the root of the auxiliary equation which is m1=2 and m2=+-2i

Q: A constant-stirred tank reactor (CSTR), initially filled with 20 kg of salt, is diluted with enough…

A: dSdt = 180s +40 S = salt concentration = 20kg s = 1% of original amount = 1% of 20 = 0.02kg

Q: 2. A population is modeled by the differential equation: *= 3N (1-) (1-) dt 50, where N(t) is the…

Q: In a liquid culture, the number of bacteria grows at a proportional rate depending on the number of…

Q: (1) When sugar is dissolved in water, the amount A that remains undissolved after t minutes…

A: We have to find the time taken for half of sugar to dissolve.

Q: The tank in the figure contains 4000 L of water in which initially 50 kg of salt is dissolved. Brine…

A: Given that, The tank contains 4000 L of water in which initially 50 kg of salt is dissolved. Brine…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

Q: A murder of crows in the wild is observed to double its population in one year. However, in…

Q: A population in a certain city in 1990 is 1.4 million people, and satisfiesthe differential…

A: A differential equation represents the relation between a variable, and it's derivative. Solution of…

Q: An ordinary differential equation of a horizontal string which is freely pinned at both ends is…

A: Given problem is :

Q: Suppose that the number x(t) (with t in months) of alliga- tors in a swamp satisfies the…

Q: What is the general solution of the first order differential equation a csc (2) – B da + a dß = 0 if…

Q: y = c1 e(-2+v3)x + c» + c2 e(-2-v/3) z

Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

Q: A large corporation starts at time t = 0 to invest part of its receipts continuously at a rate of P…

Q: What is the general solution of the first order differential equation a csc (2) - B| da + a dß = 0…

A: Given that first order diffrancial equation is αcosecβα-βdα+αdβ=0 function α=fβsolution…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

Q: Give the detailed solution of this differential equation using 1st order and 2nd order 1. (y') ² +…

A: This is a problem of differential equation.

Q: With an assumption that an insect population grows continuously and the rate of growth is…

Q: What is the general solution of the first order differential equation a csc (2) – B da + a dß = 0 if…

Q: The Pacific halibut fishery has been modeled by the differential equation * - (1-) where y(t) is the…

Q: Find the solution of the Linear Homogenous Differential Equation Cofficients. D²(D + 2)*y = 0 =D(

Q: 41. The trough in Figure 3 (dimensions in centimeters) is filled with water. At time t = 0 (in…

Q: In a chemical reaction, a compound changes into another compound at a rate proportional to the…

Q: A radioactive isotope decays at a rate proportional to the amount of the isotope, in other words…

A: Given, k = -0.283033 , let initial amount = C= 1 , final amount =A=0.5 We have to find t

Q: The population y(t) of a certain microorganism grows continuously and quadrupling time is found to…

A: In this question, the concept of the derivative is applied. Derivative We can use a derivative to…

Q: A murder of crows in the wild is observed to double its population in one year. However, in…

Q: The amount of a radioactive substance, y, decays exponentially such that its half-life is 8 days. In…

A: topic- differential equations

Q: For the differential equation y" --y' --= 0, find a particular solution which satisfies the initial…

A: To find the particular solution for the given differential equation which satisfies the initial…

Q: A 50 gallon tank is full to the brim with pure water, and 5 gallons/minute of a brine solution with…

A: Let s(t) be the amount of salt (in kg) in the tank at time t. Now, given that salt is entering in…

Question

Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped at a slower rate of 2 gal/min. If the concentration of the solution entering is 2 lb/gal, determine a differential equation for the amount of salt A(t) in the tank at time t.

Expert Solution