A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing 21b/gal of salt runs into the tank at the rate of 4 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 3 gal/min. Find the solution to the differential equation that models the mixing process.

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: The brine is entering more and going out less at rate (3 gal/min -2 gal/min = 1 gal/min), so…

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: How  can we apply second-order differential equations to the study of vibrating springs and electric…

A: Generally the equations of the analogous systems are second order differential equation with…

Q: What does the general solution of a first-order differential equation represent geometrically?

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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…

A: Let the amount of sugar in tank at time t = y(t)

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.…

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

A: Consider the radioactive decay of an isotope is given by  and the solution of this differential…

Q: The decay is basically governed by the first order differential equation = - ka is

A: We have to identify the given statement as true or false.

Q: By separating variables, find the general solution of the differential equation dvc = - dt RC' where…

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Q: The differential equation of a spring/mass system is x" +16x = 0. If the mass is initially released…

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Q: From the differential equation by eliminationg the arbitary constant A,B from y=Ae7x+Be-7x

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Q: A chemical reaction is governed by the differential equation

A: Given, the differential equation                           dxdt=K(3-x)2 where x is the concentration…

Q: Suppose a student carrying a flu virus returns an isolated college campus of 1000 students.…

A: The number of students is 1000 and the number of students who have contracted the flu is x(t).…

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

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

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Q: A tank is utilized for mixing sugar solutions which can initially contain 80 gallons of water. A…

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Q: Find the general solution of the differential equation

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Q: A car traveling at 100 km/h skids 50 m after its brakes are suddenly applied. Set up a differential…

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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: Assume that a population P of wolves in a region is proportional to the area A of the region. Does…

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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: Determine the general solution of the differential equation

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Q: Find the general solution of the differential equation.

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Q: 4. eª y – ye" 2xy?

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

A: Given Concentration=8g/m3flow rate=24m3/dayVolume=1800m3Initial insecticide concentration in the…

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

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Q: Find the order of the differential equation. And check if it is linear or nonlinear.

A: Given the differential equation

Q: Show that the differential equation below is homogeneous and find the general solution.

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Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A:

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: A student carrying an influenza virus returns to an isolated college campus with 1,000 students.…

A:

Q: A 2 kg mass is attached to a spring whose constant is 4 N/m, and the entire system is submerged in a…

A: A 2 kg mass is attached to a spring whose constant is 4 N/m, and the entire system is submerged in a…

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: How can you tell that a differential equation is separable? Thatit is linear?

A: We can say differential equation separable  if it  can be written so that all terms in x and all…

Q: A population (in thousands) grows according to the differential equation dy e ky(L-y), where the…

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Q: A body weighing 24 lb stretches a vertical spring 1 foot beyond its natural length. The spring is…

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Q: A brine solution of salt flows at a constant rate of 6 L/min into a tank that initially held 50 L of…

A: Let y be the amount of a substance. The concentration of the substance can be modeled using the…

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: In a city of a fixed population of " people , the rate of change (with respect to time t) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to time…

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

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

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: After a correct transformation of variable, a homogeneous differential equation will be reduced to a…

A: We have to check given statement true or false

Q: The population of a particular type of fish in a lake would grow logistically according to the…

A: The population of lake is given by, dydt=0.03y1−y2800 and y0=1320 To determine the number of fish…

Q: A tank is utilized for mixing sugar solutions which can initially contain 80 gallons of water. A…

A: Let the amount of sugar in the tank is "y" at any time t. Given information Tank initially contain…

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

A: topic- differential equations

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

A: We have to find the differential equation that models the system.

Q: When studying Separable DEs, we solved mixing problems in which the volume of fluid remained…

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Q: A small cannonball with mass 9 kilograms is shot vertically upward with an initial velocity of 130…

A: we have m=9, v=130, k=0.0025, g=-9.8

Q: After a murder has been committed, the body, which was originally at 37°C, cools according to…

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.