in differentials of functions, if x change by a small amount dx then, what will happen to y?

Q: A certain RNA molecule replicates every 3 minutes. Find the differential equation for the number…

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

A: We have to find the differential equation to describe growth of population y(t).

Q: A radioactive substance with a half-life of 52 days decays according to the differential equation:…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. If the…

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 the family of curves whose equation is y = X° + ax + bx + 5 given by…

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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: A virus spreading across the country is making people sick. Let x be the number of infected people.…

A: If x be the number of infected people. Then it is given that DE is proportional to the infected…

Q: What is the differential equation of the problem; The birth rate of the wolf population is 7 percent…

A: Here we have to form a differential equation.

Q: a) A maintenance staff member of the company has found that water tank is affected by some bacteria…

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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: Find the family of functions that satisfies the differential equation u′(t)+u(t)cost=cost. Use an…

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Q: What is a differential? What is it used for?

A: The differential describes a variation in the linearization of a given function. It is further…

Q: The rate of change of the population of animals is proportional to the population at a given time.…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: What is the differential equation given functions?

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Q: If the rate of change of N is inversely proportional to sec(x)- N where (-<x<). If N(O)=3, and N() =…

A: Note:- These are multiple questions and according to company guideline we can do maximum 1 questions…

Q: A fish pond has a carrying capacity of 1000 fish, and an intrinsic growth rate of 0.1, expressed in…

A: Fish pond's carrying capacity =1000 fish and intrinsic growth rate is 0.1(per year). Also, y(t)…

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

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Q: Find the y 'values and differentials for?

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Q: a- y= (cosx) (use logarithm differential)

A: To find dy/dx

Q: An object falls from rest in a medium offering a resistance. The velocity of the object before the…

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Q: The differential equation of the family of straight lines whose sum of slope and x-intercept is…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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

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

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Q: The growth rate of population of a city is known to be equal to 20% of the current…

A: According to the given information it is required to find the number of years it will take to double…

Q: The rate of change of a population of bacteria in a petri-dish can be described as the difference…

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

A: Lets suppose that the rate of change of performance with respect to time is dNdt (a) The required…

Q: The rate of change of the weight of a cow is proportional to 1200 W, where time, t, is measured in…

A: We want to find differential equation of W(t).

Q: The differential equation of the family of straight lines whose sum of slope and x-intercept is…

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Q: The differential equation of the family of straight lines whose sum of slope and x-intercept is…

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Q: A dead body was discovered shortly before midnight. At exactly midnight, the temperature of the body…

A: Let T be the temperature of the object after t hours and Let Ts be the temperature of the…

Q: Suppose we put an object with temperature T0 in a room with constant temperature K.We know that the…

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Q: If x and y are measurements of certain parts of an organism, then the rate of change of y with…

A: Formula used: The differential equation can be equivalently expressed in the form g(y) dy=f(x)dx…

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

A:

Q: Assume that the amount of time, T, a job takes is inversely proportional to the number of people P…

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Q: What do the differentials of x and y mean?

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Q: Suppose that news spreads through a city of fixed size of 800000 people at a time rate proportional…

A: Total number of people in the village are =800000. No. of people who have heard the news after t…

Q: A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 3 cm3…

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Q: Let f(t) be the balance in a savings account at the end of t years. Suppose that y = f(t) satisfies…

A: Given differential equation:- y'=0.04y+2000

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

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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: 11) Find the first derivative of y = (ln x)*

A: We have to find the first derivative of given function.

Q: en differential equation by undetermined coef y = x²ex + + 3

A: Given : The differential equation y''-y=x2ex+3. The objective is to solve the given differential…

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

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Q: The amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on 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.