A 48 gallon tank is filled with pure water. Water which has a concentration of 2g of salt per gallon flows into the tank at a rate of 3 gallons/min, and the mixture is stirred to a uniform concentration. Water also leaks from the tank at the same rate, 3 gallons/min. Find a differential equation describing the rate of change of salt in the tank.

Q: Determine the function if it is a solution to the differential equation or not.

A: Given function is a solution of the differential equation. This is a complimentary solution along…

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: Solve number 3 using first order linear differential equation.

A: We will solve the Differential equation.

Q: Find the differential equation by rlimaniting the arbitary constants from

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Q: can you give an example in real life, where differential equations are applied?

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Q: Explain when Euler’s Method produces an exact particular solution of a differential equation?

A: Euler’s Method produces an exact particular solution of a differential equation?

Q: What differential equation has general solution  y=c1e^(5t)+c2te^(5t)?

A:

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

A:

Q: The _____ of a differential equation is the power of the highest order derivative term in the…

A: The solution of above question is written below.

Q: Give the differential equation of family of lines passing through (2,0)

A: Let the equation of  line be y= mx + c Now if the line pases through (2,0) then  0= 2m + c --> c=…

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Q: What will be the order of the differential equation if its solution is y=Acos7x-Bsin7x

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Q: From the differential equation by elimaniting arbitary constant  y=ax3+bx2

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

A:

Q: If the number of fruit flies F increases at a rate that is proportional to the number of flies…

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Q: Give two examples of your own for order and degree of a differential equation

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Q: Solve the differential equation using variation of parameters

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Q: What is the differential equation of all parabolas with axis parallel to the y-axis?

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Q: True or False. Is this equation a linear differential equation of order one?

A: Given, Differentrial equation

Q: Solve the first order differential equation by separating variables.

A:

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: The _______ of a differential equation is the power of the highest orfer derivative term in the…

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: Assume that the rate of evaporation for water is proportional to the initial amount of water in a…

A: Here, given that rate of change of evaporation is proportional to the initial amount of water.…

Q: Solve using the undermined coefficient of differential equation

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

A: 1st we will make a differential equation for amount of salt in the tank and then will solve it to…

Q: Find the differential equation of family of lines whose angle of inclination is 60 degrees.

A:

Q: explain the concept of a standing wave and how it applies to differential equations

A: A standing wave, is a wave which oscillates in time whose peak amplitude profile will not move in…

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: y² = 14eax-

A: Given y2=14eax

Q: . Give an example of a nonlinear differential equation of the formy = f (y).

A: Solution: Nonlinear Differential Equation: A nonlinear differential equation is a differential…

Q: Write the first-order linear differential equation in standard form.

A: Standard form of linear differential equation is y'+P(x)y=Q(x).

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: Find the solution of the system of differential equation

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Q: A man is walking at a rate of 1.5 m/s toward a street light which is 5 m above the level ground. At…

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Q: The rate of change of the population p of bacteria at time t is proportional to the population at…

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Q: From the differential equation by elimanating arbitary constants  y=ax3+bx2

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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: What is the degree of the differential equation:

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

A: Given, Initially, the tank holds 300 gallons of water in which 50 pounds of salt have been…

Q: equation

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Q: A bowl is removed from a pottery kiln at a temperature of 200 degrees Celsius and placed on a rack…

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Q: When is an equation considered as a solution of  differential equation?

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

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Q: If an object's mass is changing at a rate proportional to its weight at a given time, does it make…

A: Two quantities are said to be proportional if they are increase or decrease in same manner. In such…

Q: Describe how to solve a first-order linear differential equation ?

A: First order linear differential equation :-  lets take an example :- y=x2+2 dydx= 2x This is first…

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.