Q3: Solve the following difference equations using Z-transforms: a) u[k + 2] + 4u[k + 1] + 3u[k] = (3)k , u[0] = 0, u[1] = 1 %3! Ans. :(-3)* b) y[n + 2] + 6 y[n + 1] + 9 y[n] = (2)" , y[0] = y[1] = 0 %3D Ans. ((2)"-(-3)"+

Q: 3. Find the solution of the following linear system by Operator method or Laplace transform method.…

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Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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Q: У" +у%3 и, (0) — из- (); у(0) — 0, у'(0) %3D 0.

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Q4: Find the solution of the simultaneous equations by Laplace transform with initial condition y(0)…

A: Here we can use the following formula for Laplace transform of derivatives of a function,…

Q: Which boundary conditions of the Sturm-Liouville problem y" + iy 0, 0 < x < 1 determine the…

A: Given,         f(x)=∑n=1∞bnsin(πnx)

Q: 5.4 Compute the Taylor polynomials Tn, n = 0, ..., 5 of f(x) = sin(x) + cos(x) at xo = 0.

A: Solve by Taylor theorem

Q: 1 The Laplace transform of the solution of the following Cauchy problem ´y" (t) − y'(t) + 3y(t) =…

A:

Q: Given the following input x[n] and Z-transfer function H[Z] for a DT LTI system X[n] = U[n], H[:] =…

A: We are given a discrete-time LTI system with discrete transfer function H(z). And we have to find…

Q: 59. By the transform method, solve Utt = Urx +h, 0 0, h = constant, Ut (x, 0) = 0, 0 0. u (x, 0) =…

A: We use Laplace transformation method to solve the given partial differential equation. Also use…

Q: 64. Use the finite Fourier cosine transform to solve the heat conduction problem t> 0, 0 0, where…

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Q: Use the Laplace transform to solve the initial-value problem: [y " +5y' +4y=2 e*, y(0) =4, y '(0)…

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Q: 6. Use Laplace transforms method to solve the initial value problem tX" (t) + 2(t – 1)x'(t) – 2X (t)…

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Q: 1 The Fourier transform of [e 2 x(t + )] is jt 1 jn( f- X(f)e#ft X(f – e"(s-±) 4 t A. O . A.…

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Q: 7. By using the Fourier transform, find a solution for the following problem (P Ju(1, x) = 4u.z(t,…

A: The complete solutions are given below

Q: Use Laplace Transforms to solve the initial value problem [y'+3y=f(x),y(0) =0] where 0Sx and x <…

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Q: Using Laplace transform to solve the IVP: y" - 5y = e", y(0) = 0, y'(0) = 0, then, we have ---…

A: As per guidelines i had solved the first question .kindly post another question separately.

Q: 4) Consider the square wave function f(x) = { 1, 0 <x<n -1, T < x < 2n a. Find the Fourier series…

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Q: 7. Use the method of Laplace transform to solve the initial value problem y" - (a + B)y' + aßy = (a…

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Q: 10. Solve the initial value problem x(t + 1)- ) xt) + () ()- x(t) + x(0) = %3D by Z-transform.

A: For the equation xt+1=1122xt+10 taking z transform of LHS and RHS:…

Q: By using Laplace transform to solve the IVP: y"-6y' + 9y = 0,y(0) = 2, y'(0) =-4 %3! Then Y(s) is…

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Q: How do I solve for the third order y''' - 4y''-11y' + 30y = 4e^8t + t^2 using the method of 1.…

A: repost the question for other method separately

Q: Solve the following initial-value problem by using Laplace transforms У"-2y'-30е^-3t, У (0)%-1,…

A: Solution of ordinary differential equation with constant coefficients: Suppose we wish to solve the…

Q: - Determine the transfer function (H(s)) of the following system using Laplace transform roperties.…

A: According to the given information, it is required to determine the transfer function H(s) using…

Q: 5. (5 points) Compute the inverse Laplace transform of 5s – 12 F(s) = s3 – 7s2 + 12s using partial…

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Q: Using Fourier transform to solve the following IVP U=2 u+te-lxl, -0 0 XX u(x, 0)= f(x) u,(x, 0) =…

A: Given: utt=2uxx+e-x;               -∞&lt;x&lt;∞ and t&gt;0 u(x,0)=f(x) ut(x,0)=g(x) utt=2uxx+e-x;…

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

A:

Q: 2. Given the nonlinear sine-Gordon eqn. Me - Sin u, u(t, r), (ut = ), k : constant (1) Also, given…

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Q: 3. (a). Use Laplace transforms and partial fractions to solve y" +4y=8t, y(0)=3, y'(0) = 0.

A: Given  y''+4y=8t, y0=3, y'0=0

Q: Suppose an undamped forced spring mass system is driven by the equation d²x di² where the Fourier…

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Q: 3.2 Use the Laplace transform to solve the following system. х" — Зх' + у' + 2x — у %3D 0 x' + y' –…

A: Given The given system is x"-3x'+y'+2x-y=0x'+y'-2x+y=0x0=0x'0=0y0=-1

Q: 1 G(s) = (s + 10)(s + 1) - Find the Z-transform of the system

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

Q: Suppose an undamped forced spring mass system is driven by the equation + 9x = f(t), dt where the…

A:

Q: 3.17 Use Laplace transforms to find the solution to the follow ing set of equations dt dy2 42 +…

A: Set of equations given as,

Q: )- 33 Use the method of Laplace transforms to solve each IVP. 5. y" - 2y' + y = 2t – 3, y(0) = 5,…

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Q: Which of the following is the Laplace transform of the solution to the initial value problem x" + x'…

A: We will find out the required Laplace transform.

Q: Please solve this differential equation question. thanks!

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Q: Use the Laplace transform to solve the given initial value problem. y(t) = 0 1 2 exp(1 t) + 1 1 -…

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Q: Find the inverse Laplace transforms of 3 f(s)=-5s+6 using a partial fraction expansion

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

Q: (1) Use the Laplace transform to solve the system of differential equations: 4x – 2y | dt2 dy 16x –…

A: Laplace transform of second derivative: The Laplace transform of second derivative of a function…

Q: By using the Laplace transform to solve the system x' = 3x - 3y + 2 = -6x-t We obtain: x(0) = 1 y(0)…

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Q: Use a LaPlace transform to determine the solution of the following systems with differential…

A: The system of differential equations is x' +4x+3y=0y'+3x+4y=2et. Apply Laplace transform: sXs-x0…

Q: By using Laplace transform to solve y +y = tet with y (0) = -2, what would the particular solution…

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Q: 15 (6- Zx) (10-3x-3») dzdydx a) convert into dxdzdy order. 0. 0.

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Q: 3) A) select the correct answer:- 1-Inverse z-transform of the system can be calculated using: a)…

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Q: 4. Solve the particular solution of y" + 3y' + 2y = 6et, y(0) = 1,y'(0) = 2, using b. Laplace…

A: Solve the differential equation, by using Laplace transferom

Q: 2. Given the nonlinear sine-Gordon eqn. ua - Sin u, u(t, z), (4 = tig), k: constant (1) Also, given…

A: Given: u(tx)=Sin u, u(t, x),  (u(xt) = u(tx)), k=constant

Q: By using a suitable Finite Fourier transform, the solution of u(0, t) = 0 u(G.t) = 0 u(x,0) =…

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Q: 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)], what special case is…

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Q: 8. Use the method of Laplace transform to solve the initial value problem y" - 2ay' + a²y = (a - 3)²…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.