A tank originally contains 100 gal of fresh water (no salt.) At time t=0, a solution containing 0.2 lb of salt per gallon begins to flow into the tank at a rate of 3 gal/min and the well stirred mixture flows out of the tank at the same rate. Set up the differential equation and the initial condition for this problem. Solve the initial value problem Do it from scratch with all the details.

Q: A bacteria colony begins with a population of 120 and quadruples in size every 1.5 days.   If the…

A: Given initial population = 120  So, for t=0, P=120  Using that we get: Quadruples in size every 1.5…

Q: The hatchery was recently bought out by a corporation and the new owners are planning on allowing…

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Q: The population y(t) grows continuously and follows an exponential behavior over time. Its…

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Q: A tank with a capacity of 250 gal is intended to be used to prepare a sugar solution. The tank…

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Q: The number of internet users in a country increases at a rate that is jointly proportional to the…

A: Let number of people having personal computer be C(constant), number of people having internet be N.…

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Q: $2. x" – 4x' +3x =te".

A: Given that x''-4x'+3x=tet To find the general solution :

Q: Give an example of a linear, nonseparable differential equation.

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Q: An investor deposits $8000 into an account that pays 6% compounded continuously and then begins to…

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Q: Make up a 2nd order differential equation that you feel confident possesses only the trivial…

A: To find- Make up a 2nd order differential equation that you feel confident possesses only the…

Q: What is a separable differential equation? How do yousolve it?

A: In a separable differential equation, we separate the variables and then take the integration of…

Q: Determine the form of a particular solution for the differential equation. Do not solve.

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Q: When predicting population growth, demographers must consider birth and death rates as well as the…

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Q: The system changed so that the right-hand side of the differential equation is 0. Use the…

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Q: What is the appropriate method to find the general solution of this differential equation?

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Q: A dropped ball accelerates downwards at a constant rate 9.8 meters per second squared. Set up the…

A: A dropped ball accelerates downwards at constant rate   9.8m/s2. Initially the ball is at height of…

Q: A stream, which is polluted with insecticide at concentration 8 g/m³, flows at a rate of 24 m³/day…

A: Concentration=8 g/m3 Flow rate =24 m3/day Volume =1800 m3 Initial insecticide concentration in the…

Q: In the mixing process given below, brine is obtained. Using the given values, obtain the…

A: Given: ri=2L/min and ro=1L/min Also, Ci=4 kg/L Consider the amount of dissolved salt over time as x.…

Q: The Detective branch from the Dhaka Metropolitan Police has come to ask you for assistance on…

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Q: Verify that the general solution satisfies the differential equation. Then find the particular…

A: Differentiating the given genaral solution we can verify if the solution satisfies the differential…

Q: The change of Turkey's population (N) over time (t) is proportional to the current population. In…

A: Note: It is assumed that the population of 2021 is being asked this question.   The general solution…

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

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Q: The management at a certain factory has found that the maximum number of units a worker can produce…

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Q: proportional to the original quantity. If there are 20 grams initially, and after 10 years, 0.6% of…

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Q: Determine whether the statement "The function y = 0 is always a solution of a differential equation…

A: Here the given statement is The function y=0 is always a solution of a differential…

Q: A falling object weighs 160 lbs. Beginning from the differential equation, find the object's…

A: Given,  a falling object weighs 160 lbs.

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

A: Given:    mg = 2    s = 1.5 inches = 1.5/12 = 1/8 feet     g = 32

Q: Suppose your bank offers 3% continual annual interest on the balance of your cer- tificate of…

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Q: A 100,000 liter tank of pure water was accidentally mixed with a 7000 liters of salt with a…

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Q: Choose the best option that describes this differential equation i) separable ii) linear iii) both…

A: Given differential equation y'=xy+xe-x2

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Q: A cypress beam found in the tomb of Sneferu in Egypt contained 55% of the radioactive carbon-14…

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Q: Initially 5 grams of salt are dissolved in 30 liters of water in a tank. Brine with salt…

A: Here Initially, 5 grams of salt are dissolved in 30 liters of water in a tank. Brine with a salt…

Q: Solve the differential equation by undetermined coefficients (annihilator approach). y(4) + y" = 3x2

A: Please see the below picture for detailed solution.

Q: A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing…

A: A tank initially contains 100 gallon of brine with 40lb of dissolved salt. A brine containing…

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A: Given, the population of a community is known to increase at a rate proportional to the number at…

Q: Assume that you can contribute $7,000 per year into a retirement fund that grows at a constant rate…

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Q: The capacity of the theater is 500 people. At a certain time, the number of people in the theater is…

A: The capacity of the theater is 500 people. At a certain time, the number of people in the theater is…

Q: A differential equation is considered to be ordinary if it has aone independent variable more than…

A: Option C  One dependent variable

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Q: A 48 gallon tank is filled with pure water. Water which has a concentration of 2g of salt per gallon…

A: Given

Q: Suppose that the population Pt) of a country satisfies the differential equation P(400 - P) with k…

A: It is given that population P(t) satisfies the differential equation-…

Q: Parents invest $28,000 in a college fund for their child and then contribute $500 per month. Create…

A: Given: The investment is $28,000. Also, $500 is contributed per month.

Q: A 100,000 liter tank of pure water was accidentally mixed with a 7000 liters of salt with a…

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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.