The side of an equilateral triangle increases at the rate of 2 cm/hr. At what rate is the area of the triangle changing at the instant when the side is 4 cm? (SOLVE BY USING DIFFERENTIAL EQUATIONS)

Q: 3 (3x? — 6ху) dx — (3x? + 2у) dy 3D0 -

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Q: Form the differential equation by elimanating the arbitary constant A,Bvfrom y=Ae7x+Be-7x

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Q: A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential…

A: The surface area of a sphere of radius r is:

Q: What is a modeling with differential equations?

A: Modeling is the process of writing a differential equation to describe a physical situation.

Q: Give an example of a linear, nonseparable differential equation.

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

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

A: Let's find.

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

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Q: What is a separable differential equation? How do yousolve it?

A: In a separable differential equation, we separate the variables and then take the integration of…

Q: solve the differential equation

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Q: Form the differential equation by elimanating the arbitary constant A,B fror V=Ae7x+Be-7x

A: y = Ae7x + Be-7x

Q: y" – y' = sint Solve the general solution of the differential equation by the method of change of…

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Q: Solve the differential equation with clear steps

A: Given, system of differential equation is dxdt=3x-y-zdydt=x+y-zdzdt=x-y+z We can write it as in…

Q: • / = Ity

A: y'=x-yx+y It is a homogeneous differential equation. Put, y=vx⇒y'=v+x·dvdx Therefore,…

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

A: Given equation is              y=Cekt

Q: Find the differential equation of all straight lines at 2- unit distance from the origin.

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Q: find the general equation of the differential equation

A: As per the honor code, we are entitled to solve only 1 question at a time so I am providing you the…

Q: Solve the differential equation by variation of parameters. у" + у %3 csc х y(x)

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

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Q: The differential equation for a freee-falling mass m near the surface of the earth is given by:…

A: Consider the equation:

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: 3. xy dx + x²ydy = 0

A: Given- xy2dx+x2ydy=0 To Solve- The above differential equation.

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

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Q: Solve using the undermined coefficient of differential equation

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Q: 25.y' — х — 4ху ; х—D0, у3D 1/2

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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: Describe the difference between the general solution and a particular solution of a differential…

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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: Solve the differential equation by undetermined coefficients (annihilator approach). y(4) + y" = 3x2

A: Please see the below picture for detailed solution.

Q: A man takes 40 mg of a certain medicine. Each hour, the amount of medicine in the man’s system…

A: Given , man takes 40 mg of medicine and each hour medicine decreases by 30%. We need to calculate…

Q: Find the relative error in the computed area of an equilateral triangle due to an error of 3 percent…

A: To find the relative error in measuring the area of equilateral triangle where the edge is measured…

Q: arcsin(y'(x)) – x = 0 con y(3) = 5, es

A: Conversion of  differential equation into voltera integral equations

Q: If the rate of change in the number of cows, W, in a population is proportional to 150 - W(t), where…

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Q: Find the serial solution of the differential

A: We have to find out the series solution of the differential equation y''-xy=0 at the neighborhood 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: If an error of 1 percent is made in measuring the edge of a cube, what is the percentage error in…

A: Take the formula of the volume of a cube then differentiate it to get the error in volume.

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: oM Differential Equation Show a complete solution ySy 13yty =0

A: Consider the given homogeneous equation.

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: aur + 2xyury + y*uyy = 0

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Q: Match the differential equation with the appropriate slope field. y' = O A) B)

A: Note: We know that, the slope field is a visual representation of the solutions of a first-order…

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

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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