Show that the Euler-Lagrange equation for the functional 1 S[y] : + y² + 2xy)dx, y(0) = 0, y(1) = a, where a is a constant, is y" - y = x

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: dw Find the value of- dt at the point (1, In 2 ,0) on the curve x = cos t ,y= sin t, 0 <t< 2n where…

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Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y%3D 2x . -5 dy

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Q: Use the differential dy to approximate Ay when x changes as indicated. y = V3x – 2; from x = 2 to x…

A: Topic - approximation Using derivatives

Q: Let y = 2 T. Find the change in y, Ay when x =1 and Ar = 0.2 Find the differential dy when x = 1 and…

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Q: Let dy/dx =f(x, y)= x^2 -y Use Euler’s method ( with step size ℎ = 1) to approximate the value of…

A: Given, dydx=f(x,y)=x2-y y(0)=1 h=1

Q: What is the differential equation of the orthogonal trajectories of the family of curves X = Cy? А)…

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Q: Let w = x2e2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y =…

A: Given: w=x2e2ycos3z x=cost y=lnt+2 Putting x, y and z in w, we get…

Q: Let y = 3x2. Find the change in y, Ay when x = 2 and Ar 0.2 Find the differential dy when x = 2 and…

A: We have to find solution

Q: Let y = 2 T. Find the change in y, Ay when x = 1 and Ax 0.2 0.190 Find the differential dy when x =…

A: please see the explanation below

Q: Use the method of reduction of order to find a second independent solution of the given differential…

A: Use reduction of order method

Q: Find the differential equation for the family of parabolas with axis parallel to the x-axis and with…

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Q: Let y = 3/x. Find the change in y, Ay when x = 2 and Ax = 0.1 %3D Find the differential dy when x =…

A: We have to find change in y and differential dy.

Q: Let y = 5 x. %3D Find the change in y, Ay when a = 5 and Ax = 0.3 %3D Find the differential dy when…

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Q: Let y = 4x. %3D Find the change in y, Ay when x = 5 and Ar = 0.4 Find the differential dy when x = 5…

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

Q: Find the differential dy of the given function. y = (x + 1)/(2x − 1)

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Q: Show that f(x, y) = ln(x2 + y2) solves Laplace's equation, ∂2z ∂x2  +  ∂2z ∂y2  =…

A: Given Laplace’s equation is

Q: Show that the function y =  A e-x    + B x e-x satisfies the differentialequation y"   +2y' + y  =0

A: The given differential equation is y''+2y'+y=0. Let y=Ae-x+Bxe-x. This implies that,…

Q: The solution of Laplace equation d'u = 0, where 0 < x < 3 dx? and 0 < y < 2 with boundary conditions…

A: Step:-1 Since we know for Laplace equation if step size h= k then ui, j=14ui+1, j + ui-1, j + ui,…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = (x+1)/(3x-5)   dy=

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Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,…

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Q: Find the differential dy of the function y = Provide your answer below: dy = dx 5x4 + 4 4x + 3

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Q: Let y = tan(4r + 8). Find the differential dy when a = 3 and dæ = 0.1 Find the differential dy when…

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Q: Let y = 5,a. %3D Find the change in y, Ay when r = 5 and Ar = 0.2 Find the differential dy when r =…

A: Our problem is let y=5√x First, it is easiest to take the derivative of this when in a different…

Q: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

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Q: Let y = 2 /T. Find the change in y, Ay when x = 1 and Ax = 0.3 %3D %3D Find the differential dy when…

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Q: Find the potential P(x,y) attached to the exact ODE 2x sin(y) +x² cos(y) y' = 0

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Q: Let y = tan(3r + 4). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: The two-dimensional Laplace equation, = 0, describes potentials and steady-state temperature…

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Q: Let y = 5√√. Find the change in y, Ay when x = 2 and Ax = 0.1 Find the differential dy when x = 2…

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: Let y = f(x), where 3x? f(x) : Зx + 4 ,2 x + 4 Find the differential of the function. dy =

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Q: Find the differential dy of the given function. y = √x +1/√x

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Q: Let y = (x + 3). %3D Find the differential dy when z = 2 and dz = 0.2 Find the differential dy when…

A: Given:  y=(x2+3)5  Differentating y with respect to xdydx=ddx(x2+3)5Using differential power rule…

Q: Write the differential dw in terms of the differentials of the independent variables. w =…

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Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

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Q: Find the differential dy of the function y Provide your answer below: dy= dx = 5x4 + 4 4x + 3

A: y=5x4+44x+3Differentiate w.r.t xdydx=4x+320x3-5x4+444x+32

Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Linear measurement is one-dimensional. A linear differential equation is an equation where the…

Q: Let y = 4.x?. Find the change in y, Ay when x = 1 and Ax = 0.4 Find the differential dy when x = 1…

A: Given: y=4x2 To find the change in y, ∆y  x=1 and ∆x=0.4

Q: Use the differential dy to approximate Ay whenx changes from x = -2 to x = -1.96. %3D y = x² + 1

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Q: Let y = 3/. Find the change in y, Ay when x = 1 and Ax = 0.1 Find the differential dy when x = 1 and…

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Q: Find the second order differential of the function y=e2u, where u=u(x).

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Q: Find the second order differential of the function y=u3, where u=u(x).

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Q: Let z = f(x, y) = 2xy + x. Write the differential dz in terms of x, y, dx, and dy. %3D

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Q: Verify the Pierre-Simon Laplace equation ∂2f/∂x2+∂2f/∂y2=0 with f(x,y)=ln∣x2+y2∣

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Q: Let y = e, find the differential dy Select one or more: a. e2x O b. e2x dx O c. xe* dx Od. 2xe dx

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Q: Let y = 3x². Find the change in y, Ay when x = 1 and Ax 0.1 Find the differential dy when x = = 1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…