Use the Laplace transform to solve the given initial-value problem. [t, 0≤t<1 t≥ 1 y' + 6y = f(t), y(0) = 0, where f(t) 10, y(t) = +

Q: 5, show your solution for the Laplace Transform of the function of G (t), G(t) = t, G(t) = 10 0 4

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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: Use the Laplace transform to solve the given initial value problem. For technical reasons, write u…

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Q: Let f(x) = r e-t dt – 1/2. Find root to f(r) by using bisection method. You should find the interval…

A: As the given integral is improper and have no closed form solution; we will use numerical…

Q: Consider the function I(7) defined by: 1 I(7) = Jo -t/T dt What is 4?

A: Given function is  Iτ=1τ∫0∞e−t/τ To find dIdτ

Q: Use the Laplace transform to solve the initial value problem: 0St<3 (-5, y(0) = 0, y'(0) =-1 y +9y=…

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Q: Let t2 f(t) = if 0 1. For x > 0, define F(x) = f(t) dt. (a) Find F(1) and F(2).

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Q: y" - 5y + 6y = 6(u₂ (t)-us(t)) y(0) = y'(0) = 0

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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: Find  d/dt [ w(t) ]^2 and show that it equals 2w(t)w'(t)

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Q: (2+31) Simplify (7-4i) 16)

A: We have to simplify the following -  (2+3i)(7-4i)

Q: transformada de Laplace

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Q: 7) Use the Laplace transform method to solve the Volterra integral equation: u(x) =1-x - (x -t u (1…

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Q: Use laplace transform to find the initial value problem of; y'+y=f(t), y(0)=0; f(t)={0, 0or=1}

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Q: y (t) = 1- y(t-r)e e*dr , y(0) = 1 -2r

A: To solve the below equation using the Laplace transform. y't=1−∫0tyt−τe−2τdτ, y0=1

Q: C. Time Differentiation. Determine the Laplace Transform of y(t) given all the initial conditions…

A: We have to solve the given problem by Laplace transform technique.

Q: Evaluate / Vx2x/x +1 dx: /2x/x + I dx: 3 (2x + 1) + C 중 금(2xi + 1)' + C + 1) + C 5 (2x3 + 1) +C

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Q: 3. Determine the Laplace transform of f(t) = uz(t)(t − 3)³e²−3.

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Q: 2.Use the Fundamental Theorem of Calculus Part 1 to find the derivative of the functions 17 yt a)…

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Q: у"(С) — бу'(t) — 2y(€) = 4 cos 2t – 4t³; y(0) -2, y'(0) = = -

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Q: y"(t) + 7y (t) + 6y(t) = 6(t – 3), %3D y(0) = 0, y (0) = 0.

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Q: Find a function f that satisfies the equation | f(t) dt = 2 cos x + 3x – 2. %3D -

A: Derivative of a definite integral is: ddx∫0xf(t)dt=f(x) Formulae used: ddxcosx=-sinxddxx=1ddxC=0…

Q: Find the Laplace transform, F(s) of the function f(t) = 9t² - 8t + 7 F(s) = s> 0

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Q: psin z F(#) = [" t cos(t) dt (1) (a) . Compute F(T). Let

A: The solution are next step

Q: Use the Laplace transform to solve the given initial-value problem. y"+y= √2 sin(√2t), y(0) 13,…

A: Solution:-

Q: 1. Calculate the Laplace transform of the function when 0 <t<1 when 2 <t<3 everywhere else 1-t f(t)…

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