(a) Compute the average temperature of a wire in the shape of a helix c(t) = (cos(t), to, sin(t)), t e [0, 107]| if the temperature at the point (r, y, z) in R³ is given by T(x, y, z) = 2x² + ev +22?

Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge-Kutta method, what is…

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Q: (a) Find the differential dy. y = cos(xx) dy = -T sin (Tx)dx (b) Evaluate dy for the given values of…

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Q: Find the differential dy of the function y = 3x ' O a) dx b) 3x dr c) x 4 In(3) 3 d) dx e) 글x dx

A: We are given y =3x^(1/4)  To find dy just differentiate y with respect to x

Q: Find the particular solution of the Initial value problem (I.V.P) : yˊˊ + 16 y = - sin4t 2. Verify…

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Q: The heat transfer rate of the rocket engine is given by: dT Q = -kA- dx Where k is the thermal…

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Q: (a) Find the differential dy. y = tan(x) dy = (b) Evaluate dy for the given values of x and dx. x =…

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Q: 1 Let y = -. Find dy and Ay at x = 7 with dx = Ax = – 1. Enter the exact answers. dy = Ay =

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Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

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Q: (a) Find the differential dy. y = rad(15+x2) (b) Evaluate dy for the given values of x and dx. x =…

A: a)   The given function is y=15+x2. The differential of y is,…

Q: Q1-Use the chain rule to express dy / dx in terms of xand y: 1-1 a) y = аnd x = at 1= 2 1+1 b) y=1-…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: The differential equation dx/dt = 100x(x- 5)+ s models a population with stocking at rate s.…

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Q: Given the linear differential operator L = D² – 8D + 41, find a function y(x) below such that Ly =…

A: Given that: L = D2 - 8D +41 To find: A function y(x) such that Ly = 0 First we find the factors of…

Q: In a mass-spring-dashpot system , the mass’s position at time t isy = 4e-t(sin t - cos t), t ≥…

A: Given: y=4e-tsint-cost, t≥0 The average value of y over the interval 0≤t≤2π

Q: (a) Find the differential dy of y = e#/5. (b) Evaluate dy for a = 0, dx = .1. (a) dy = dx (b) dy =

A: Solved below

Q: 4. The current i(x, t) along a submarine cable of length L satisfies ixx RCi 0<x<L, 0<t = di -(0, t)…

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Q: 02:- a. b. Let u=x²-2xy + 2y³ with x = s² lnt and y = 2st³. Find ou/Os and du/ît. find the total…

A: In this question, we want to find the partial derivatives and total derivatives of the given…

Q: The exact differential d(xy)= xdy+ ydx , what is the d O= 4x²y°dy+ 2xy*dx.

A: Find your answer below

Q: (a) Find the differential dy. y = et/4 - Ap (b) Evaluate dy for the given values of x and dx. x - 0,…

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Q: 1 Let y = -. Find dy and Ay at x = 8 with dx = Ax = –1. х Enter the exact answers. dy = Ay =

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Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: In the given DE, cos z + In y + ( +e) dy 0, de integrating M (x, y) with respect to x generates a…

A: Here we are given a differential equation And we have to find the function g(y). For this first we…

Q: 3. Prove that the IVP dy x- = cos(xy), y(1) = 2, dx has a unique solution curve locally near the…

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Q: (a) Find the differential dy. y = 5 tan x dy = (b) Evaluate dy for the given values of x and dx. x =…

A: Formula used:  ddxa.x=a.ddxx ddxtan x= sec2x

Q: 1 Let y = -. Find dy and Ay at.x = 7 with dx = Ax = - 1. Enter the exact answers. dy = Ay =

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Q: (a) Find the differential dy of y = x² + 2x + 5. (b) Evaluate dy for x = 3, dx = 1/2. (а) dy 3 dx…

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Q: y3 (b) Solve the integral . (cx – y)dx + (2x + y)dy along the curves x = from (0,0) to (1,1)

A: The given problem is to evaluate the given contour path integral over given path x=y3.

Q: a) Find the differential dy. y = ex⁄2 dy = ? (b) Evaluate dy for the given values of x and dx.…

A: Explanation of the answer is as follows

Q: (a) Find the differential dy. y = cos(Tx) dy = (b) Evaluate dy for the given values of x and dx.…

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Q: (a) Find the differential dy. y = cos(TX) dy = (b) Evaluate dy for the given values of x and dx.…

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Q: Let y = tan x. (a) Find the differential dy. (b) Evaluate dy and Δy if x = π/3 and dx = -0.2…

A: Let,  y=fanxa To find differential dy, differentiate y       with respect to x,        dy=sec2x dx

Q: (a) Find the differential dy of y= /4+ 5x. (b) Evaluate dy for æ = 0, dx = .04. (a) dy dx (b) dy =

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Q: (a) Find the differential dy. y = tan(x) dy = sec?(x) (b) Evaluate dy for the given values of x and…

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Q: In an integro-differential equation, the unknown dependent variable y appears within an integral,…

A: Given, dydt+4∫0tyt-we-4wdw=3, y0=0 a) Taking Laplace transform of the above equation…

Q: a)  Find the differential dy. y = cos(?x) dy = ?       (b)  Evaluate dy for the given values of x…

A: We have to find the following given conditions according to the given condition

Q: (a) Find the differential dy. V3 + x2 dy = (22+3)() (b) Evaluate dy for the given values of x and…

A: Given query is find the differential of y and its value.

Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: (a) Find the differential dy. y x +1 dy = (b) Evaluate dy for the given values of x and dx. x = 1,…

A: Find the differential of the function and then put the value.

Q: Let C be a positively oriented smooth curve with interior D. A function f : R² → R is called…

A: Given: ∫C∂f∂ydx-∂f∂xdy ∂2f∂x2+∂2f∂y2=0

Q: The total differential of g(x, y) = e*z²-y is at A(1,4) is %3D Select one: a. dg(A)=(8-1)e^(0) O b.…

A: Consider the following function: gx,y=e4x2-y Differentiate gx,y with respect to x taking y as…

Q: 6. The electric potential at each point (x.y) in the region R: 120.ys1 is given by V=…

A: The electic potential function is given by: V=48xy-32x3-24y2 To locate the maximum and minimum of it…

Q: (a) Find the differential dy. y = e/3 dy = (b) Evaluate dy for the given values of x and dx. x = 0,…

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Q: (a) Find the differential dy. y = V3 + x2 dy = (b) Evaluate dy for the given values of x and dx. x =…

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Q: 3. Find the total differential of the ff. at (1, -1). f (x, y) = 3.x² + y² – xy %3D

A: Solution:Givenf(x,y)=3x2+y2-xyFormula:d(xn)=nxn-1

Q: Q2:- a. b. Let u=x²-2xy + 2y³ with x = s²ln t and y = 2st³. Find au/as and au/at. find the total…

A: We need to solve the two questions.

Q: 3. Evaluate the total differential of the below equation at (x, y) = (16, 24), where dx = 1.5 and dy…

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Q: dy When reduced to a linear DE of order one in z, the Bernoulli's equation +yl-)= 3x3y² becomes dx…

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Q: (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y =…

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Q: Given (1 + 3x sin y) dx - x² cos y dy=0 with y(1) = 0. Using Euler or Runge - Kutta method, what is…

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Q: Find the differential dy of the function y=(cos(x))(7x) a. dy=-7x(sin(7x))dx b. dy=(-cos(x))(7x)dx…

A: To Find the differential dy of the function y=(cos(x))(7x)

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.