According to the differential equation: T'=0.1T(1-T/1000)-0.05T What are the equilibrium values and which ones are stable/unstable?

Q: What is a particular solution of a differential equation?

A: Particular solution: particular solution of a differential equation is obtained by known value for x…

Q: What function satisfies the differential equation y - y' = 0?

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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: what is the Non-exact differential equation?

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Q: Find an energy function for the differential equation y"=-y3

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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: Write down a first order differential equation for the current in an LR-circuit to which a voltage…

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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: In y = C₁e* + C₂е¯x

A: Given problem:- Find its differential equation through eliminating arbitrary constants.    In(y) =…

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: When predicting population growth, demographers must consider birth and death rates as well as 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: y = Ae* + Be-*

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Q: Write the differential equation satisfied by y = Cekt.

A: Given equation is              y=Cekt

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: What is a first-order linear differential equation?

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Q: The linear Differential equation of any order if there is no constant term s present is known as?

A: We have given The linear Differential equation of any order if there is no constant term s present,…

Q: Find the solution y(t) by recognizing the differential equation

A: Given differential equation - y' = 6300-yWe can write it as - dydt = 6300-ydy300-y = 6dtIntegrating…

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: Form the differential equation by elimaniting the arbitary constant A,B from y=Ae7x+Be-7x

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

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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: To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t)…

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Q: Which are the differential equations and initial conditions?

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Q: The rate of growth of a plant is proportional to the difference between its height h and the maximum…

A: The given data is: The rate of growth of a plant is proportional to the difference between its…

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: 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: Determine if the function is a solution of the differential equation y''-y=0

A: y''-y=0 y'' represents the second derivative  we find the roots , by writing the given equation in…

Q: The differential equation dP/dt= (k cos(t))P, where k is a positive constant, models a population…

A: An variable seperable ordinary differential equations of first order can be solved by table same…

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

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Q: Please solve differential equation A - By = dy/dx A and B are constant.

A: The given problem is to solve the given differential equation where A,B are given as constants.

Q: What is a first-order differential equation? When is a function a solution of such an equation?

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Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

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Q: Which kind of the differential equation is it

A: dydx=y' = x2y+y3x3+y3 is the given differential equation.    Degree of Numerator =3  Degree of…

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

A: topic- differential equations

Q: What is the degree of the differential equation:

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Q: The rate of growth of wild horses is proportional to 2000 – H, where H is the number of horses and…

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

Q: What does it mean for a function to be a solution to a differential equation?

A: A function is said to be a solution of differential equation if it satisfies the differential…

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: 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…