(c) Model (not Solve) the system of differential equation if two connected tanks as tank-1 contains 1000 gal of water in which initially 200 kg of cement are dissolved and tank 2 contains 1500 gal of water in which initially 300 kg of cement are dissolved. Fresh water runs in the tank-1 at the rate of 100gal/min. The mixture is pumped from each tank to the other at the rates that is 150gal/min from tank-1 to tank-2 and 50gal/min from tank-2 to tank-1. In addition, the mixture flows out from tank-2 at rate 100 gal/min.

Q: 3.  Brine containing 3lb/gal of salt enters a tank at the rate of 4gal/min and the solution…

A:

Q: 5. In previous problems dealing with two species, one of the animals was the predator and the other…

A: (b) we have given the system A dxdt =-5x+2xydydt =-4y+3xy we have to determine all the equilibrium…

Q: 4x2y'' + 4xy' - y = x1/2 +ln2x Solve the differential equation. (State the equation models in the…

A: Find CF and PI using Euler methods

Q: (a) Model (not Solve) the system of differential equation if two connected tanks as tank-1 contains…

A:

Q: Find the particular solution of the differential equation that satisfies the initial equations. f…

A: ∫xn dx =xn+1n+1+C ∫1x dx=ln(x)+C

Q: Find the particular solution of the differential equation that satisfies the initial equations. f…

A: Topic = differential equation

Q: The population of a certain country is known to increase at a rate proportional to the number of…

A: It is given that the rate of increase of the population of a country is proportional to the number…

Q: Carbon decays at a rate proportional to the amount present. The percentage lost is 5% in 150 years,…

A: The percentage lost is 5% in 150 years, if the carbon vanished in 1000 yearsTo find: the beginning…

Q: 5. A 400 gallon tank initially contains 100 gallons of fluid in which 50 pounds of salt is…

A:

Q: A tank has pure water flowing into it at 12 liters/min. The contents of the tank are kept thoroughly…

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Q: Choose differential equation that you believe best models the rate of change of the amount of salt…

A: We need to determine which of the given equations best models the rate of change of the amount of…

Q: A watering system holds 500 gallons of water. Water is added into the system at a rate of 8 gallons…

A:

Q: A 500-gallon tank originally contains 100 gallons of fresh water.  Beginning at time t = 0, water…

A:

Q: 3. A certain population of bacteria has an initial count of 100. If the population grows in a…

A: The population at any time t can be obtained by the equation Where, P0 is the initial size of the…

Q: general solution of the differential equation y^2 y' = 2e^x  b ) particular solution (if it exists)…

A:

Q: A differential equation and one of its solutions, y1  is given. Use the method of reduction of order…

A:

Q: if roots of linear second order differential equation is real than general solution will contains…

A: Topic = differential equation

Q: 2. Single-Tank Mixing a) Write an initial value problem to model the following situation: A tank…

A: Since you have posted a question with multiple subparts according to guildlines I will solve first…

Q: A vat with 500 gallons of beer contains 4 % alcohol ( by volume ). Beer with 7% alcohol is pumped…

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Q: A 190'F bottle of milk left in 60 F room. At time initially the milk is cooling at 4 'F per minute.…

A:

Q: 5. Initially, two large tanks A and B each hold 100 gallons of brine. The well-stirred liquid is…

A: Given- Initially, two large tanks A and B each hold 100 gallons of brine. The well-stirred liquid is…

Q: A population of bacteria grows logistically. Suppose that the initial population is 3 mg of…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: wasp population has a 10 percent birth rate and a 7 percent death rate. Every year people swat an…

A: Given query is to find the differential equation for the problem.

Q: A slow economy caused a company’s annual revenues to drop from $530, 000 in 2008 to $386,000 in…

A:

Q: Radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of radium…

A: From given, the time is t = 100 yr, the initial amount of radium is No = 100 mg and the final amount…

Q: A tank contains 350 liters of fluid in which 45 grams of salt are dissolved. Brine containing 5…

A: The problems related to the concentration of the liquid in a tank can be solved using the first…

Q: The given family of functions is the general solution of the differential equation on the indicated…

A: Solution :∴ y''-y =0    , y(o)= 0,   y'(0)=1given family of solution is y = C1ex+C2e-x

Q: A tank contains 350 liters of fluid in which 45 grams of salt are dissolved. Brine containing 5…

A:

Q: A solution containing 2lb of salt per gal starts to flow into a tank of 50 gal of pure water at a…

A: Given that, A solution containing 2lb of salt per gal starts to flow into a tank of 50 gal of pure…

Q: Application of First-Order Differential Equations 1. A body falls from rest against a resistance…

A: (Note: We are entitled to solve only one question at a time.) Given: A body falls from the rest…

Q: A tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of salt at time t…

Q: 11. A fish tank initially contains 800 grams of oxygen dissolved in 200 liters of water. Water…

A: Given information  200 lt     = Total volume of water 800 gm = Initial amount of Oxygen in…

Q: A. Sketch the zero isoclines of the system B. Determine all the equilibrium solutions of the…

A: This is the question from stability of a system.

Q: With Solution) Find the particular solution of the differential equation (y²- x²)dy - 2xydx = 0;…

A:

Q: A differential equation and one of its solutions, y1  is given. Use the method of reduction of order…

A: Given equation,x2y'' - x(x+2)y' + (x+2)y = 0x>0y1x=xyx=ux y1xyx=ux

Q: tank contains 6L (liters) of water in which is dissolved 32 g (grams) of a chemical. A solution…

A: Let's find.

Q: A pair of differential equations has the solution x(1) = -2²¹-et, y(t) = -221 +e™! with initial…

A: Here we find the system of linear differential equations by taking the general form of it. And…

Q: Differential Equations Problem: In 2015, the foreign debt of the Philippines is Php 2950.00 billion.…

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Q: Application of First Order Differential Equation A body of unknown temperature is placed in a…

A:

Q: A small metal bar, whose initial temperature was 20°C, is dropped into a large tank of boiling…

A: First we formulate differential equation by given condition rate of increase rate of temperature .…

Q: solve partial differential equation r-4s+4t=0

A: Given PDE is r-4s+4t = 0

Q: (3y²-x² ()y' -=0 ;when x = 1, y = 1 2y4

A:

Q: || 3. cx² + y² = 4

A: The given equation is  cx2+y2= 4  We have to find the differential equation from this given…

Q: Also find the solution of the differential equation that satisfies the initial condition…

A: (a). The given differential equation is: x2y'+xy=4

Q: Two different concentrations of a solution are separated by a membrane through which the solute can…

A: Note:- In given problem, some signs are missing in given equation. So, please check equation i'm…

Q: (a) Consider a fish population, assume that the total number of fish is constant. Some of fish live…

A: according to question, assume that the total number of fish is constant say M let Rt denote the…

Q: A small metal bar, whose initial temperature was 20° C, is dropped into a large container of boiling…

A: The given question can be solved as explained in step 2.

Q: Consider a system of differential equations describing the progress of a disease in a population,…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.