In the presence of a uniform electric field a charge accelerates     indefinitely.     until it reaches the speed of light.     only if the initial velocity of the charge has a component parallel with the electric field.

Q: Obtain the differential equation of the family of lines passing through the center of the conics…

A: First find out the centre of given conic then write the equation of family of lines passing through…

Q: What is the solution of a 2nd order homogeneous linear ODE whose roots of the characteristic…

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Q: Use the direction field to sketch the graphs of the solutions that satisfy the given initial…

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Q: Refrigerant 134a enters a well-insulated nozzle at 200 lbf/in.?, 200°F, with a velocity of 120 ft/s…

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Q: Let x(t) be the displacement of an object, attached to a vibrating vertical spring with one end…

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Q: Show that the set of solutions of a second-order linear homogeneous differential equation is…

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Q: Suppose a 32-pound weight stretches a spring 2 feet. If the weight is released from rest at the…

A: In this question, we set up the differential equation for the given data and then solve by using…

Q: is exact or not. If yes, then solve the initial value problem of this equation with initial conditic…

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Q: This is a differential equations problem.

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Q: When a mass of 4 kilograms is attached to a spring whose constant is 64 N/m, it comes to rest in the…

A: Solution :-

Q: For an object in damped harmonic motion with initial amplitude a,period 2π/w,and damping constant…

A: Given  An object in damped harmonic motion with initial amplitude a,period 2π/w,and damping constant…

Q: When a mass of 2 kilogram is attached to a spring whose constant is 32 n/m, it comes to rest in the…

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Q: Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that…

A: Concept: The two expressions connected by equal to be called an equation. The expression on the two…

Q: Consider the spring-mass system whose motion is governed by the differential equation d?y dy + 2a +…

A: Consider the spring mass system whose motion is governed by the differential equation:…

Q: A spring is stretched 6 in by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism…

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Q: Consider a system of two toy railway cars (i.e., frictionless masses) connected to each other by two…

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Q: Specifically a DiffEq problem. Question in pic below. Answer: (1/16)pi(2n+1), n = 0, 1, 2, ...

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Q: Match the third order linear equation with their fundamental solution sets.

A: m3-7m2+10m=0⇒mm2-7m+10=0⇒mm-2m-7=0Solution set , 1,e5t,e2tD   m3+m=0⇒mm2+1=0⇒m=0 , m=±iSolution…

Q: A 16-lb weight is attached to the lower end of a coil spring sus-pended from the ceiling and having…

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Q: Use computer software to obtain a direction field for the given differential equation. Sketch an…

A: Given:       y dy/dx = -x       y(1) = 1

Q: A 2 kg mass is attached to a spring with spring constant k = 200 N/m. The mass is displaced 2/3…

A: Answer is mentioned below As mentioned, have provided the solution for d and e

Q: To model the spread of a disease in a population of size N, the differential equation model = (kb -…

A: Here, dldt=kb-cl-kbNl2

Q: A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

A: We have to find the equation of motion for given condition.

Q: When a mass of 3 kilograms is attached to a spring whose constant is 48 N/m, it comes to rest in the…

A: we have to find equation of motion .

Q: If e* and xex are solutions of y"tay'tby=- Are soluhons linearly independent? write the soluhion.…

A: Given that e−x and xe−x are the solutions of y''+ay'+by=0. We have to check whether the e−x and xe−x…

Q: if the mass is initially released from a point 1 meter below the equilibrium positon with an upward…

A: We will find the equation of motion as shown below

Q: State the order of the partial differential equation -3uxx = 5uy + 10u + 5. Then classify whether it…

A: Given the partial differential equation is -3uxx = 5uy + 10u + 5 ⇒ 3uxx + 5uy + 10u + 5 = 0…

Q: Find the particular solution that satisfies the initial condition.

A: Afghan

Q: A certain vibrating system satisfies the equation u" + yu' +u = 0. Find the value of the damping…

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Q: To model the spread of a disease in a population of size N, the differential equation model == (kb -…

A: aTo model the spread of a disease in a population of size N,thedifferential equation…

Q: 1 A spring is such that a 4-lb weight stretches it 6 in. An impressed force; -cos8t is acting on the…

A: We have to determine the position of the weight as a function of time x(t).

Q: A 1-kg mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

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Q: 1. Find the root of system of equations using Newton Method. Employ initial guesses of x=y=1.2…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: A 1-kilogram mass is attached to a spring whose constant is 24 N/m, and the entire system is then…

A: NOTE: Refresh your page if you can't see any equations. . mass is m=1 kg the spring constant is k=24…

Q: Solve the initial value problem Ut + 2uz = 1, x € R, t e R u(0, x) = e¯*, x € R. %3D

A: The differential equation is given as ut+2ux=1 The Lagrange equation is given as dt1 = dx2 = du1 On…

Q: Two particles A and B, of masses 0-3 kg and 0-7 kg, are moving towards each other on a smooth…

A: Given that masses of particles are                                                      mA=0.3…

Q: Use the SlopeField command in GeoGebra to obtain a direction field for the differential equation…

A: We shall use the commands given in the question to plot the direction field and the solution curves…

Q: 8.A certain vibrating system satisfies the equation u″ + γu′ + u = 0. Find the value of the damping…

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Q: If C, and C, are constant vectors and A is a constant scalar, show that H - e* (C1 sin Ày +C2 cos…

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Q: A model for the velocity v at time t of a certain objoct faliling under the influence of gravity in…

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Q: Recast the system of higher order differential equations as a first order system. u""=2u-3v…

A: The given higher order differential equations are: u'''=2u-3vv''=3tu'v'-cos u Recast the system as a…

Q: 3. A model for the velocity v at time t of a certain object falling under the influence of gravity…

A: The equation of the certain object in viscous medium is given by dv/dt = 1 - v/8

Q: a. Find the solution to the heat equation

A: Given,            ∂u∂t=16∂2u∂x2,                t≥0,   0≤x≤5                   ...(1) u(0, t)=u(5,…

Q: A certain vibrating system satisfies the equation u" + yu' + u = 0. Find the value of the damping…

A: In this question, The second-order differential equation is given. u''+γu'+u=0 To find the damping…