Use the Laplace transform to find the solution x(t)

Q: Use Laplace transform to solve for y(t) : t* y(t) = t²(1 – e-t). |

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Q: Find the Laplace transform of: f (t) = e-2t sin t

A: Given; f(t)=e-2tsint

Q: Solve the Laplace Transform of the equation f(t)= sin3t/t

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Q: Show the derivation of the Laplace transform for f(t) = u(t).

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Q: 4. e sin 2t

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Q: 2 sin 4t t

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Q: Find x(t) and Y(t) using Laplace transform.

A: The given pair of equations dxdt=2x-3ydydt=y-2xx0=8, y0=3

Q: Use the laplace transform to solve 3x'-y=2r;x'+y'-y=0; x(0)=y(0)=0

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Q: Solve for the laplace transform x(t) = (t+3) sin(t-6)

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Q: Solve the ODE using the Laplace Transform method: x" + 4x = 1+t; x(0) = 0, x'(0) = 2

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Q: 5. x(t) = 5 – 2t

A: Given function is x(t) = 5 - 2t

Q: 3t x(t) = to

A: We have to apply the Laplace transform of the given function.

Q: Find the laplace transform of f(t)=2t^2 e^-t - sin^2 t

A: We have to find the Laplace transform of f(t)=2t2e-t-sin2t .

Q: Solve using the Laplace transform y' - y = e3t , y(0) = 2

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Q: Solve the Laplace Transform f(x) = 2/x

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Q: 10. x(t) = t sin bt

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Q: Find the Laplace Transform L (e-t sin t)

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Q: Find the Laplace transform of (t2 + 1)2.

A: we use the formula £(t^n)=n!/Sn+1. See 2nd step.

Q: 6. Solve for the Laplace transform of f(t) = t^2 using the long method

A: Given that: f(t)=t2

Q: Use the laplace transform to solve 3r'-y=21;x'+y'-y=0; x(0)=y(0)=0

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Q: Derive the laplace transform for f(t)= 3 e-St

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Q: Use the Laplace transform to find x(t) and y(t)

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Q: Solve the Laplace transform. L[ t3sin 2t]

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Q: 3. f (t) = t³

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Q: Find the Laplace Transform of the function f(t)= e-t ^ sin ^ wt

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Q: Use the definition of a Laplace Transform to find L[f(t)]. f (t) = e-5t

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Q: Using the Laplace transform, compute t * e-t * e', where indicates the convolution.

A: We will find out the required value.

Q: f(x) = = 1 2 cos: X x

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Q: * - 10x + 9x = 5t, x(0) = -1, x(0) = 2

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Q: f(t) = 2Ct -4)

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Q: f (t) = cos2

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Q: Solve the initial value problem using the Laplace transform.

A: Given initial value problem is y'''(t)+5y''(t)+9y'(t)+5y(t)=t2ety(0)=0, y'(0)=0, y''(0)=-2…

Q: Determine the Laplace Transform of the function and evaluate f(2i)

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Q: Find the Laplace transform Y

A: Given,        y''+4y=t0≤t<111≤t<∞'   y(0)=9,  y'(0)=4

Q: Determine the laplace transform of f(t) = sin8t sin 6t

A: We find the Laplace transform of  f(t)=sin(8t)sin(6t)

Q: Find the Laplace transform of f (x) = e* sin2x %3D

A: Let us consider a function f(t) then the Laplace transform of f(t) is given as L[f(t)]=F(s) Some of…

Q: Determine the Laplace transform of the function f(t) = (t + 2)².

A: We need to determine the Laplace transform of the function: ft=t+22.

Q: Find the Laplace Transform of the function f(t) = 1

A: Here given  f(t)=1

Q: Find the Laplace transform of the equation. a and b are constant.

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Q: Determine the Laplace transform of the function F(t) = t^l.5 exp{-2t}.

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Q: 1. x(t) = 3t5

A: Given Function: x(t)=3t5 constant multiplication property of Laplace Transform:…

Q: Find the inverse Laplace transform of H(s) +ed

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Q: Use the Laplace transform to solve x'-2y'=1;r'+y-x=0;x(0)=y(0)=0

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Q: t² - te' +e"cost 4t

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Q: 2. Solve for the Laplace transform of f(t) = 5 using the long method

A: A detailed solution is given below

Q: 2e3t – 3e3t

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Q: Find the Laplace transform of f(x)=x

A: This question is related to Laplace transform.

Q: Solve for the laplace transform using the formula. 9. F(t) = e-2t-

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Q: solve using laplace transform: f(t) = sin(t/5)

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Q: Find the Laplace transform of f(t) = te-t from the definition.

A: Here we use the definition of lapses transformation.