Exampley Consider the following nonlinear sine-Gordon equation Utt-Uxx+5 inu zo subject to the following intial conditions: U (x,0) = 0 , Ut(2₁0)=43echx 1 Using Adomian decompostion Methode.

Q: -1 -1 6s-5 4s²+7] 3s-2 s²+8s+25]

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Q: 2. Consider the differential equation (2 − x²) y" + 2xy′ – 2y = 0 (a) Verify that y = x is a…

A: Given differential equation is 2−x2y''+2xy'−2y=0.....1. a We have to verify that y=x is a solution…

Q: 10 Given the polar equation r= 5-2 sin 8 a. find the eccentricity and identify the type of conic; b.…

A: given the polar equation r=105-2sinθ (a) find the eccentricity and identify the type of conic. (b)…

Q: Sketch the region bounded by the given lines and curves. Then express the region's area as an…

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Q: Q₁: (A) Let R be a ring with identity. Define g: Z → Z by g(x) = x. 1, Vx € Z. Is g a homorphism?…

A: Ring homorphism

Q: (B) Let G be a set of all real numbers except 0. Define on G by a b = |a|b, where lal is the…

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Q: Let I'be the volume of the parallelopiped formed by t ã= a‚Î + a₂j+ak

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Q: Solve the differential equation

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Q: Q3: (A) Prove that 1. There is no simple group of order 200. 2. Every group of index 2 is normal.…

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Q: Determine the value of k if the L[ tkt ] = 1/(s2 - bs + 6.0).

A: Solution

Q: L [3²+ 3s 5² +45+13 २ ·]

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Q: 2 2 ď 1¹ [²³²375] = 0²³² +² t (8-373

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Q: 2. Find the maximal interval of existence and uniqueness of the solutions to y' = eV¹- guaranteed by…

A: Please see the attachment

Q: OB + - - . — (x − ¹)² 2 (x − 1)³ + −6 (x − 1)4 24 (x − 1)³ + - ¸ + + + 3! 5! 720 (x − 1)² + 1) -5040…

A: Given :  The given expression is ;   00!+x-11!+ -x-122!+2x-133!+-6x-144!+24x-155!+ -120x-166!+... To…

Q: @ Fs [ f(x)} = -P Fc {f (x)} ap 2 proof: H.W.

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Q: 2.) - 5y = e-³t sin(4t); y (0)=3, y' (0) = 10 dt

A: Some Laplace formulas

Q: Determine the value/s of D if the graph of the equation x² + 4y² + Dx − 4y + 2 = 0 an empty set.

A: Fact :- Sum of squares is always non negative

Q: 1- y = -y² 2yt+1 2rv y(1) = -2

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Q: dx 4√/3x-x² 5³-

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Q: Provide the equation of a sphere of radius 5, centered at the origin, in: 1. rectangular coordinates…

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Q: Determine whether the series. converges conditionally, converges absolutely, or diverges: 1 1 1 1 +…

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Q: Let C₁ be the line segment from the point (-4, 8) to the point (2, -4), C₂ be the arc on the…

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Q: Please don't post this question on google 10 Given the polar equation r = 5-2 sin 8 a. find the…

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Q: rmine the half-range cosine expansion of the given periodic function: t, f(t) = {₁ - t 0<t<π/2…

A: Half range cosine series expansion

Q: Jse Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

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Q: Find the Fourier Integral Representation of (0 f(t) = t 0 t1

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Q: 1. Determine the half-range cosine expansion of the given periodic function: f(t) = { ₁-t₁ t,…

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Q: 1. There is no simple group of order 200.

A: Solution:-As per guidelines I submit first question only

Q: g(t) = -{ = t², -8 + 3t, (t− 6)² + 2 cos (²-1), 0 2

A: Solution

Q: 3. Determine the Fourier integral representation of the given function: f(t): { 0 < t <3 otherwise =

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Q: Given are the following nonlinear equation -2.x 4x²-36=0 two initial guesses, x, = 1 and x₁ = 4, and…

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Q: Q: Define the concept of the ring. Is (Z+.) a ring? What's about e' (Z, +,.)?

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Q: Using the stability criterion by means of bilinear transform (Tustin), find if the system is it…

A: Given : F(z) = z4-z3+0.5z2+0.5z+0.5a0 = 1a1 =-1a2 = 0.5a3 = 0.5a4 = 0.5Finding stability :1. an =…

Q: II. Assign the given vehicle trips (veh/hr) using incremental method (n = 3). 35 D) E 15 14 20 16 21…

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Q: This question is about the function f(0) = (0 - 3) cos(0). (a) Explain why the graph of f lies on or…

A: Solution. :-

Q: dvanced Math 1. Find solution of the system of linear differential equa tion.. Use matrix method. 4…

A: Given system of differential equation is ,                    X' = 411141114 X On comparing with  X'…

Q: raw a line segment 6 inches long. Subdivide it according to the golden ratio. Verify your work using…

A: We have to a draw a line segment 6 inches long and subdivide it according to the golden ratio.…

Q: Q4: (A) Prove or disprove each of the following 1. Every prime ideal is maximal. 3. The cancellation…

A: Each and every option is false. We disprove them by giving appropriate counter examples. The…

Q: Q₁: (A) Let R=(Z12, +12-12). 1. Find all maximal ideals of R. 2. Evaluate char. (R). 3. Is R a…

A: Solution:-

Q: 1. Determine the half-range cosine expansion of the given periodic function: t, f(t) = {₁-t₁ 0<t<π/2…

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Q: 1. Given the function f(x) = 400x5-900x* +657x³ - 200x² + 25x + 0.2 with integration limits from a =…

A: We are given f(x)=400x5-900x4+657x3-200x2+25x+0.2 a=0, b=0.8, n=5 (five segment) then…

Q: Find the closest line to the points (1,4.5), (3, 4.5), and (4,1). Identify the following components:…

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Q: What is integration?

A: We have to define the term integration. Integration:- The antiderivative of a function fx is called…

Q: Solve the differential equation y'(t) - 2y(t) = e2t; y(0) = 1.3. What is the value when t = 1.20?

A: Given differential equation is ,                             y'(t)-2y(t) = e2t   ;     y(0) = 1.3…

Q: Consider the vector field Ĥ(x, y, z) = (y², x, z²). Let S3 be the portion of the paraboloid 2 = x² +…

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Q: Find the range, mean or average deviation, variance and standard deviation of the following grouped…

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Q: S f(x,y)dA It posits only in the region bounded by; the x-axis, y - 2 = 0, www y + x - 5 = 0 and x =…

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Q: This question is about the function f(0) = (0 - 3) cos(0). (a) Explain why the graph of f lies on or…

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Q: A loan of $2000 is being amortized over 48 months at an interest rate of 12% compounded monthly.…

A: Given information Loan amount=$2000 Interest rate r=12% Monthly interest rate R=12%12=1%…

Q: Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by…

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