y(0) = 1, y'(0) = −2 y" + 8y = 0 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation 0 Now solve for Y(s) = A B and write the above answer in its partial fraction decomposition, Y(s): + Y(s) = s+a s+b Now by inverting the transform, find y(t) = + where a < b

Q: -3(1-cosh 377t) t

A: We are given : -3(1-cosh 377t)t Let, f(t)=-3(1-cosh 377t)t Now, L-3(1-cosh…

Q: Find the charge q(t) on the capacitor and the current i(t) in the given LRC-series circuit. 5 2244…

A: Solution:

Q: -2s+6 -1 s2 +4

A: If Lf(t)=F(s), f(t) is called the inverse Laplace transform of the function F(s).…

Q: b) Find the inverse Laplace transform of the following function: 3s +6 F(s) = s² +9s + 5.

A:

Q: f(d) = e-2d d4

A:

Q: Use the Laplace transform to find the general solution to y′′−y =0.

A:

Q: 3y +y = 3y2 Inx

A: ANSWER :

Q: Determine the inverse laplace transform of the following: (s+2)² 4 s²-1 s+6 82+9

A: As per the given instruction, we shall use MATLAB to find the inverse Laplace transforms for the…

Q: Find the transform of the function: g (t) = t3/2

A: The objective is to find Laplace Transformation of the function gt=t32

Q: Determine the Laplace transform of the following function f(x) = x2 1. f(x) = e®, a E R 2.

A:

Q: t3 - 3t2 + 5t – 8

A:

Q: F(s) = 8 $³-3s²-4s 00

A:

Q: Please do the Fourier transform of the following formula u₁(xo, Yo) = exp(- exp(-xo+yo) wo

A: Given: u0x0,y0=exp-x02+y02w02 To find: Solution

Q: Derive the Laplace transform of the following functions: s-a L{et cosh (bt)} = (s-a)²-b2

A: The given laplace transform  is ℒ eatcosh (bt)=s-a(s-a)2-b2

Q: Find Laplace transform for the function f(t) = 3 sin 4t .

A:

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

A:

Q: 35-1 F(s) -

A: The given function isF(s)=3s-1s2+25

Q: * + 3x + 6x = 0, x(0) = 0, x(0) = 3, x(t) =?

A:

Q: Use the definition to find the Laplace transform of functions to follow

A:

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

A:

Q: F(s) = 1 (s + 1)²(s² + 4)

A:

Q: F(s) = s4+s-6

A: Given F(S)=(5)/(s2+s-6). We need to find the inverse Laplace transform .

Q: Write the general equations for the following: a. Laplace Transform b. Fourier Transform

A: The Laplace and Fourier transformation are two important integral transformations with kernel one.…

Q: Solve the following Laplace Transform of Algebraic Expression: 5. Finf the L t?e-3t ? Show Solution.

A:

Q: sinudu

A:

Q: Derive the general formula for the Laplace transform of the following functions:

A:

Q: Evaluate the Inverse Laplace Transform F(s)= s+ 3s + 2

A: Problem is solved using concept of inverse laplase.

Q: Find Laplace transform by definition f(L(T)) = e-107

A: We have to find Laplace transform of given function using Definition.