1. A particle moves along the x-axis according to the equation x-2+3F, where x is in m and is in second. Calculate the instantaneous velocity and instantaneous acceleration at -3s.

Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)xy is an…

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Q: Find the solution of the differential equation that satisfies the given initial condit du dt 2t +…

A: The given differential equation:                                          dudt=2t+sec2(t)2u…

Q: 3.u 3.Use differentials to approximate the value of v99.4

A: In this question we have to find the approximation value of 99.4

Q: 14. A particle moves along the x-axis so that its acceleration at any time t is a(t) = 2t - 7. If…

A: Given that, A particle is moving along the x-axis so that its acceleration at time t is a(t) = 2t…

Q: Match the appropriate slope field with the differential equation y'=+2. 事 B.

A: given differential equation y'=xy2+2 claim- to find the slope field of the given equation definition…

Q: 1. Find the differential dy in y= 2x4-3x3-5x 2. Use differentials to find approximate values for…

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Q: Write down a differential equation of the form =ay + b whose dy dt solutions all approach y = 6 as…

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Q: A firm has the Cobb-Douglas production function y = 10x}^^x!7²x}^. Currently, it is using the input…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A: Here we find the first order differential equation of given function.

Q: 4. A 2 kg mass is attached to a spring whose constant is 6 N/m, and the entire system is submerged…

A: Given: X(0)=2-4 ∴2-4=C1-11+C2-131 2=-C1-C23,    -4=C1+C2 The required solution is…

Q: b. Using differential equations, find the orthogonal trajectories of the following family of curves:…

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Q: Suppose that we are interested in the amount of salt (in kg) at a certain moment in time, denoted by…

A: To solve the given statements

Q: 3. (D³ – 3D² +4)y = 40cos2x + 6

A: Given, D3-3D2+4y=40 cos2x+6 Its auxiliary equation is, m3-3m2+4=0⇒m+1m-22⇒m=-1,2,2 Hence,…

Q: The number of customers in a store is modeled by the function P that satisfies the logistical…

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Q: Find the Bolution to Hhe initial value problem - Please Write the folution with the computer.

A: Solution of Linear Differential Equation with Constant Coefficients: The general form of linear…

Q: 15. Use differentials to approximate V26.

A: To approximate263

Q: You can think of the first two cases as being performed in vacuum (no friction) and air of water…

A: Let's find.

Q: For an ideal gas, the pressure is related to temperature and volume by the formula 8.31T . If your…

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Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: Consider the direction field of the differential equation dy/dx=xy-8)- 7-9. y 7 YND but do not use…

A: Given dydx=x(y-8)2-6 We know that slope of linear equation id the it's derivative So, m=dydx

Q: Compute for the initial velocity of 3÷(cos(45)×38. Show your complete solution

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Q: Which differential equation is associated with the following direction field? 2 0 Oy (y-1)(y - 3)…

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Q: Verify that the function y = Ce5x is a solution of the differential equation           y′ = 5y

A: The given function is  y = Ce5x  The differential equation is y′ = 5y

Q: (1 point) Solve the following initial value problem: dy + 3y = 3t dt %3D with y(1) = 3. (Find y as a…

A: To solve the following initial value problem

Q: (64 – 2) dy = 1, y(0) = 9 Solve the initial-value problem for y as a function of x. %3D da

A: We need to solve the initial-value problem 64-x2 dydx=1, y0=9 for y as a function of x. So,…

Q: What is the differential equation of the orthogonal trajectories of the family of curves x2 - 3xy-…

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Q: Solve the ODE x²y" + xy' +| y = 0 about a singular point 16

A: We need to solve ODE.

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQ ( 1. (D³ - 5D² + 3D + 9)y = 0 2. (D³ - D² –…

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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: Utt - c?uxx = 0, – %3D

A: We have to solve the given equation utt-c2uxx=0   .......(1) The given condition are…

Q: Solve the following Initial Value Problem. dy/dt=sec^2(t)-sin(t), y(pi/4)=1 y=??????????????????

A: Given that: dydt=sec2t-sint, yπ4=1

Q: According to the Ideal Gas Law, the pressure P, temperature T, and volume V of a confined gas are…

A: We have to use differentials to approximate the percentage change in pressure if the temperature of…

Q: Find the differential equation of the quartics : c^2y^2 = x ( x - a )^3 with c held as fixed.

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Q: Jesaki Inc will sellN units of product after spending $a thousand in advertising, as given by N = 73…

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Q: 15. Find the equation of the tangent line to the curve at point (0, In 2). * y = In(e* + e4r) 2y +…

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Q: 1. Eliminate the arbitrary constants on the given equation: y = A + Be*

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The amount u of a radioactive material change in time given as a differential equation du dt = -7u…

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Q: Find the terminal value, lim y (r), for the solution of differential equation dy + 3z'y - 6z". dr

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Q: 2) If a particle is moving in a straight line, and its distance away from its starting place (in…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

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Q: Use a linear approximation (or differentials) to estimate the given number. e−0.01

A: Let f(x) = ex, where x = –0.01. Then f(0) = 1.

Q: Solve the initial-value problem for y as a function of z. (64 – ) = 1, y(0) = 2 dy da

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Q: solve the Initial Value Problem using Separation of Variables. y' = cos2x, y(0) = π/4

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Q: Solve the initial-value problem for yy as a function of xx. (64−x2)dydx=1,y(0)=5(64-x2)dydx=1,y(0)=5

A: (64-x2)dydx=1⇒dy=dx64-x2integrating,                ∫dy=∫dx64-x2+c      [c=…

Q: Use Newton-Raphson method to solve the following simultaneous nonlinear equations assuming x(0) =…

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Q: QUESTION 4 Given f(x) = 8x³ + 2x. Estimate the value of ƒ(2.01) using differential. %3D

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Q: (1/4) Estimate the value of 82 a. approximation b. differentials

A: To estimate the value of 8214 by using a approximationb differentials

Q: What is the differential equation of the orthogonal trajectories of the family of curves X2 -…

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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: 3) 1 Use an integrating factor to solve dy - by 25/4 = X with y(i)=-2

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