Using the Laplace transform, obtain the solution x(t) of the Initial Value Problem (a) + 4x = 0, where x(0) = 10 and (0) = 0

Q: Using an appropriate transform, solve the following Integral Equation: ƒ(t) − f(t − T)re²² H(T) dr =…

A: Step 1: The laplace transform can be used to solve the given integral problem, which is a…

Q: Consider the function | dt, defined in [-2, +). Find the local max/min of f(x).

A: Local maxima and minima  Use lebnitz theorem for differentiation

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: 1 | t(t + 3) dt -1

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Q: Let F(s) = 1 (2s − 1) (2s − 3) - Find f(t) = L-¹[F(s)]

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Q: Use the Laplace transform to solve the following ODES: (a) + 3x + 2x = 0 (b) + 2x + 2x = 0 Solve…

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Q: A2 Use the Fourier Transform Method to find the solution u(x,t) of the initial value problem: ut +…

A: Solve for u(x,t): We now have:U(ω, t) = F(ω) * e^(-iωt^2/2)Invert the Fourier Transform to obtain…

Q: 2- Solve the fractal differential equation Day + y = 5e²x With a = a = and and y(0) = 1, Using…

A: Given Fractal Differential Equation:  Where ​ and .Objective: To solve the given fractal…

Q: Use the Laplace transform to solve the initial-value problem, y" + 4y = 1-u(t − 1); y(0) = 0, y'(0)…

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Q: If f(t)dt = 1, S g(t)dt = 3, evaluate (3f(t) + 2g(t) – 5)dt.

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Q: (a) Find the LRT of Ho: a = 1 versus H₁ a 1 based on sample X₁,..., Xn from N(0, a0), where is…

A: As per our guidelines I can solve only first question. Kindly post the remaining question again…

Q: Using the Laplace transform, obtain the solution r(t) of the Initial Value Problem (b) 2x + 2x + x =…

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Q: Hx) =) x? +13 9=6 ccx)=?

A: We have to find  linearization L(x) of f(x)

Q: Using the Laplace transform, obtain the solution r(t) of the Initial Value Problem (c) + x = 3 *…

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