The elasticity of demand of a service is gìven by E(q) = 1 - (p + 1)+, where E(g) = Dª/ [note that q' is 9/dp]. .bd Create a first order variable separable differential equation from the above equation.

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: Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters…

A: Given problem:- Find the general solution of non-homogenous differential equation using Variation of…

Q: determine the general solution to thegiven differential equation. Derive your trial solution…

A:

Q: The weight of a population of yeast is given by a differentiable function, W, where W(t) is measured…

A:

Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

A:

Q: Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters…

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Q: A spring is stretched 175 mm by an 8-kg block. If the block is displaced 100 mm downward from its…

A:

Q: The order of the differential equation of all circles of given radius a is: 3 2

A: Let's find.

Q: A certain drug is being administered intravenously to a hospital patient. Fluid containing 5 mg/cm3…

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

A: We have to find out the amplitude of vibrations of given equation

Q: 9. From the differential equation sinh 2x, sketch some of the family of curves. %3D dx

A: Given differential equation, dydx=sinh(2x)dydx=e2x-e-2x2∫dy=∫e2x-e-2x2dxy=e2x+e-2x4+C

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

A:

Q: By using suitable method, form an ordinary differential equation by eliminating constant A from the…

A:

Q: Consider a very large tank filled with 200 liters of fresh water at time t = 0. Suppose that brine…

A: The initial conditions we have are  Initially, tank has 200 litres of freshwater. i.e.  V(t=0) = 200…

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: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

Q: he population y(t) of a certain microorganism grows continuously and follows an expo uadrupling time…

A: In this question, the concept of derivatives 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…

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Q: Find the differential equation of all circles with radius 1 and centers on the line y = x.

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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: From the differential equation by elimaniting arbitary constant y =ax'+ bx²

A:

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: Obtain the differential equation associated with the given non-derivative equation in x and y. Show…

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Q: By using suitable method, form an ordinary differential equation by eliminating constant A from the…

A:

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 bank pays continuous compounded interest. Sue deposits $100 in the account and in 3 years she has…

A: We will find the equation of A(t) as following.

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

A:

Q: Is the differential equation x" + e^x - 1 = 0 conservative or non-conservative? Explain why? If it…

A: Given x''+ex-1=0

Q: In a city of a fixed population of "P" people , the rate of change (with respect to timet) of the…

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

Q: A body with an initial mass of 200Kg is in motion under the action of a constant force of 2000N.…

A:

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

A:

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

A:

Q: Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters…

A:

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

A:

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: If the family of curve has 3 arbitrary constants then the corresponding differential equation is a)…

A: See solution below

Q: Suppose that the population P(t) of a country satisfies the differential equation dP/dt= kP(200 - P)…

A: dPP(200-P)=kdt∫dPP(200-P)=k∫dt1200∫dPP-∫dP200-P=k∫dtInP-In(200-P)=200kt+cInP200-P=200kt+cP200-P=ce20…

Q: 2) Obtain the differential equation of parabolas with vitex and focus on the x-axis

A: To find: the differential equation of parabolas on the x- axis.

Q: 13. Obtain the differential equation of the family of straight lines at a fixed distance p from

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Q: In a certain tropical forest, “litter” [dead vegetation like leaves and vines] forms on the ground…

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Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

A:

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: If the family of curve has 4 arbitrary constants then the corresponding differential equation is c)…

A:

Q: A culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to be…

A: Let P(t) be the number of bacteria present at time t.Given that the growth rate is proportional to…

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: 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…

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.