5. Let y(t) be the solution of intial-value problem y"- 2y + 10y=f(t), y(0), y(0)-8 where f(t) = (2-4). 04t23 34t Find the laplace transform y(s) of the solutions y(t), Find the Laplace transform f(s) of the forcing f(t). Do not take the inverse Laplace transform to Find y(t). Just solve for y()

Q: Question* The Laplace transform of f(t) = et-2 cos(2t-4) u(t- 2)-e-(cos(3t) - 1)

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Q: Question 4 Find the gradient of the function at the given point. w = 2x - 4yz+z², (1, 1, −2) 21+…

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Q: When calculing the Laplace transform of the function f(t)=e^2t.sin(4t) is obtained as a result:

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Q: 7. Using Lyapunov functions, show that the origin is unstable for the ODE i = -x3 ÿ = -y3

A: The solution is given below

Q: -t 82 Find the L.T of f(t) = 36² ² + 4 sin 6t -t ~Y Given :- f(t) = 3e-² + usinst - + 4 sinbt ] 1:5…

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Q: Which of the following is NOT a possible solution for Laplace's equation? (a) y = (AePx +…

A: Laplace equation is second order partial differential equation. Laplace equation in two dimension…

Q: Find the Laplace transform F(s) = L {f(t)} of the function f(t) = (3 – t) (u₂(t) — u₁(t)) F(s) = L…

A: Formula of Laplace transform  Lu(t-c)=e-cssLtkf(t)=(-1)kdkdsk(F(s))

Q: Solve using Laplace transform y"-2y' +5y=1+t, y(0)=0, y'(0)=4

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Q: Separate variabies and use partial fractions to solve the initial value problem. Use either the…

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Q: 1) x(t) = 1(t- 47T)

A: Solution 1: Given function is x(t)=1(t-4T)           (1) Let the z-transform of x(t) is X(z)…

Q: 3) x(t) te-at 1 4) x(s) = (Sta)2

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Q: Find Laplace transform of the function f(t) = cos(2t + 3)+e¬'u(t – 4) + tcosh²2t

A: Use the following formulas while calculating the Laplace transform of the given function.…

Q: 2s2 +13s+6 Find the inverse Laplace transform of H(s) = (s+2)2(s-1) assuming that a) h(t) is causal…

A: We will find out the required inverse Laplace transform of H(s)

Q: Which of the following statement(s) are true? Choose only 2 statements. Lütfen bir ya da daha…

A: The solution is given as

Q: 8. State the transformations applied to y = f(x). a) y = -3f(x) b) y = f(2x) – 7 c) y = f(-x) d) y =…

A: Given function  y=f(x)

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: (x + 3)³ 12 16 11 f(x) Consider the function 4(х — 1)2 4 1 (x – 1)2 4. Note that - (x – 9)(x + 3)²…

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Q: Solve for the inverse Laplace Transform of 8 F(s) 53 - 3s2 – 4s 8 f(t) = – 2t + 2 a. + te4t Ob. 8…

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Q: Consider the following. w = xy2 + x2z + yz?, x = t2, y = 5t, z = 5 (a) Find dw/dt using the…

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Q: (t², 0st<2 Find the Laplace transform of F(t) - 5, t2 2

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Q: 1. Deduce the continuous function whose Laplace Transform is 10 F(p) P (p² + 9) 2.Find Р2—ЗР+10 (i)…

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Q: Determine each of the following derivative values that involve functions that are defined in terms…

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Q: 1. Let F(t) = (e¹−¹ – ť², 3t² + 1, 4-5 lnt), G(1) = (-6, 1,0), and f(t) = cost. Evaluate: (a) (F-G)…

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Q: ƒ(s) = 4s - 18 9-s² What function f(t) has Laplace transform: 5s (s - 2)² +

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Q: y -7y +10y= 9cost+7sint, 5, y =-4 2

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