Use Laplace transform to solve the following initial-value problem. У" - 2у +5у%3D1+t;y(0)3 0;y' (0)%3 4

Q: Find the 1st derivative of the following. Differentiate implicitly. Simplify your final answer but…

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Q: How to solve this equation y''' - 8y" + 4y' +48= 4x2+1 using Laplace Transformation.

A: Converting the equation in Laplace transform:…

Q: (28x if |x|1* Find the Fourier transform of (x) = { %3D

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Q: Find the derivatives of all orders of the functions

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Q: 3e-2t, where x(0) = *(0) = 0 Q2. Find the response of a system * + 5x + 6x = a. Obtain the transfer…

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Q: (:) X1 + 2x2 2x1 + x2 X1 + x2 Let L: R? → R³ be defined by L Let B1 and B2 be ordered bases for R?…

A: Remark: Let L : Rn -> Rm be a linear transformation, then the matrix representation of L will be…

Q: 4. f(t) = e^(5t)(t^3) A. 6/ (s-5)^4 B. 6/ (s+5)^4 C. 6/ (s-5)^3 D. 6/ (s+5)^3 %3D

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Q: Question 2 Apply the linearity to find the transformation a) f(1)-1+r b)/(0)-2- <)(1)-2-…

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Q: Laplace Transform. Please show your complete solution

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Q: using Laplace transform. S=10h 'T=coh Ft = ht+by - banjos (8)

A: The given differential equation is:y''-4y'+4y=4cos2t;  y0=2,  y'0=5. We have to solve using Laplace…

Q: Use Laplace transform technique to solve y +2y +2y= e-, y(0) = - 4, y'(0) = - 2

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Q: (hex) = (7x-6x³) 9 2) 3) x+1 x-1 x√x+1

A: Find the derivative

Q: Show that d(w) - = [6(w− 1) + 6(w+1)] is the Fourier transform of cos(t). Show that d(w) = −ix[8(w −…

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Q: 2e 5(s+1) (a) Determine I |(s+4)' ` s² +2s +5 3.

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Q: 3. f(t) = [sin(2t)]^2 %3D

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Q: Use Laplace transformations to solve the IVP y" – y' = 0 - y(0) = y'(0) = 1 Show the complete…

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Q: suppose that we only know that g(1) = −4 and g′(x) = √(x^2 + 3). Calculate the linear approximation…

A: NOTE: Refresh your page if you can't see any equations. . take x=1 . and the given point is

Q: 13. x" = -2x + 2y, y" = 2x - 5y; x(0) = 2, x ' (0) = 3, y(0) = 1, y' (0) = 2

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Q: x^2y′′ + (3/2xy′ + [(1/36)x^2/3 − 7/144]y = 0 z = (1/2)x^1/3, w = yx^1/4 Solve it using the…

A: The transform method can be used to find the solution to the differential equation x^2y′′ + (3/2xy′…

Q: Q3. (a) Consider the continuous function f(t)=sin(2xnt). i) What is the period of fſt)? ii) What is…

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Q: 2. f(t) = -7(e^3t)[sinh(2t)] A. -14 / (s^2 – 6s + 5) B. (-7s + 21) / (s^2 – 6s + 5) C. -14 / (s^2 -…

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Q: Tx – 2VT+ V3 (2x2 – x) (3x - 2) - - Find D Do not use logarithmic differentiation.

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Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: 2. Let 2s6 s³3s2 + 4s - 12 Find the inverse Laplace transform, y(s). Y(s):

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Q: 5. 2y"+3y"-3y'– 2 y = e',

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Q: Use Laplace Transform to find the solution of the IVP 1. y"-10y'+9y=5t ---y(0) and y'(0)=2

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Q: 5. Find the general solution to x₁ = 4x₁ + 2x₂ + 3et, x₂ = 2x₁ + x₂ + et using Laplace transform.

A: The given system of differential equation is  x1'=4x1+2x2+3etx2'=2x1+x2+et To find the general…