Problem: Using the language of differential forms, find the value of the integral of the vector field A = (2+z³)0, + y²0, +2xzo, along the curve C:I->> x(t)=(1-1) sint² y(t)=1+e-e z(1)=2¹-1

Q: Consider the slope field shown. (a) For the solution that satisfies y(0) = 0, sketch the solution…

A: Given, the slope field:

Q: Consider any(n) + an-1y(n-1) + + a1y' + aoy = f(x) where an, ...a1, ao E R, where an 7 0. ... (a)…

A: consider anyn+an-1yn-1+.....+a1y'+a0y=fx            ...i where an, ......., a1 , a0∈ℝ where an≠0 (a)…

Q: Integrate f(2)= 3Re(2) counterclockwise around the unit circle, using Cauchy's integral theorem if…

A: I have given the answer in the next step. Hope you understand that

Q: Write only the corresponding differential operator of y''+8y'-8y=0

A: The general form of linear ordinary differential equation of order n is yn+a1xyn-1+......+anxy=qx.…

Q: 6. Let F = (4e" cos(4x), e sin(4x) + 2y) be a vector field and let C be a curve in the first…

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Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: 2. Which of the following equations describes the given slope field? Explain your reasoning. (a) y'…

A: Here is the solution of the given problem. Sketching of slope field.

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: y"" - 4y" + 5y' - 2y = 7t-5, y(0) = 0, y'(0) = 0, y'(0) = -2

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Q: Minimizing the length of the residual vector r = b – Ax is equivalent of mini- mizing the quadratic…

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Q: Use Laplace transforms to solve the differential equation: y' +y – et = 0 where y (0) = 0, y (0) = 0

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Q: Sketch the slope field for dy/dt = y sin t for −2π ≤ t ≤ 2π, −2 ≤ y ≤ 2.

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Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: Let f(t) be the velocity in meters/second of a car at time t in seconds. Give an integral for the…

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Q: Find the local linearization of f(I) = 1/1 at-3. %3D Ls(z) =U %3D

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Q: 1. Use isoclines to sketch the direction field for y' = x+ 2y and sketch the solution curve that…

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Q: How do I solve the laplace(u(t-2)cos(t-2))

A: The Laplace transform formula for translation on the t-axis is given by ℒ{u(t-a) f(t-a)} = e-asF(s),…

Q: Calculate r' (t) and T(t), where 88.8 r' (t) = ( T(t) = ( r(t) = (3t6,2 - 3t, 2t - 9).

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Q: Prove f(x,y)=ln(x2+y2)1÷2  by laplace equation

A: Given: The function, fx,y=lnx2+y2 and the Laplace equation, ∂2f∂x2+∂2f∂y2=0.

Q: Find the gradient field of the function, f(x,y,z) = (2x² + 2y² +2²) -1/2

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Q: (a) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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Q: (b) Find x(1) by using Laplace transform and inverse Laplace method of following differential…

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Q: Solve the differential equation by using Laplace Transformation od? y" - y = g(x) f1, x 3 (0) = 1,…

A: According to the given information, it is required to solve the differential equation using laplace…

Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

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Q: (а) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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