3. f(t) = t°e^(-4t) 4. f(t) = (e^(10t)) sin(2t)

Q: What is the Laplace transform of y’’ – 6y’ + 15y = 2 sin (3t), with y(0) = -1 and y’(0) = 4

A:

Q: SOLVE FOR INVERSE LAPLACE TRANSFORM 3s + 2 4s2 + 12s + 9

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: メ - Hx = 8 ; t-0,メ=? %3D

A: Given x.-4x=8  at t = 0 , x = 2

Q: 7. Use the Laplace Transform to solve the IVP y +2y - y -2y= sin(3t) ,y(0) = 0, y'(0) = 0, y'(0) =1

A: We have to use Laplace Transform to solve IVP.

Q: Use the Laplace transform to find the solution to the given initial value problem.  Please refer to…

A: Consider the given initial value problem:

Q: Find the Fourier transform of S (x) =!-\,| sin x dx Hence evaluate

A: Given,    f(x)= 1-x, x≤10        , x>1

Q: Solve the equation dy y ху-з dx II +

A: The given equation is of the bernoulli's equation form.

Q: Find the Laplace transform of L(t5)

A: The Laplace Transform of f(t) is given by, L{f(t)}=   ∫∞ 0   e^-stf(t)dt Here f(t)=t^5 So, L(t^5)= ∫…

Q: Solve by Laplace transform 4 -zt )ycn) yCt-u)du -te

A:

Q: Q5. Find the Laplace Transform of the funcetions x(t) and yit), which satisfy the coupled first…

A:

Q: Solve for the Laplace transform of f(t) = 5 using long method. %3D

A:

Q: Find the Fourier transform of -at TE|< 1 fCE) = otherwise

A: We have to solve the given problem.

Q: 1 Find the Inverse Laplace Transform of s2+2s+ 10 -'cos3t B -Isin9t 3 cost 9 -'sin3t (D 3

A:

Q: 7. Given that the Laplace transform of te is F(s) =- (s + k) Laplace transform of te" without using…

A: The solution is given as

Q: 4. Solve for Laplace transform of f(t) = t^5 using long method

A: This question is based on Laplace transform formula.

Q: Find the Laplace transform of 4 sin(3t)+2 cos(9t).

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: fCt = [ Htu (t-π) Jun (37)

A: As per the question we are given the following function : f(t) = [1+u(t-π)]sin(3t) And we have to…

Q: the Fourier transform of a continuous time signal x(t) is X(ja), then, the Fou ansform of the signal…

A: Given, Fourier transform of a continuous-time signal                                   x(t)  ↔…

Q: Using Laplace transform, solve dy a + 6y = 3sin(2t) with y(0) = 1 and determine y(1) in 4 decimal…

A:

Q: Q2) Solve the initiai value problem by Laplace transform. y" +4y=cos 2t y(0) = 1 , y'(0) = 1

A:

Q: Solve The fallowing funcbions by using Laplace transformahions

A: Solve by using Laplace transfer

Q: 1. f(t) = cos(6t)

A:

Q: 5 sinh (3t) +4 cosh (3t)

A:

Q: In general, if two functions have the same Laplace transform, these functions cannot differ over an…

A: Solution

Q: Find Lf" sin /6t-r'e"}

A: Please see below

Q: Compute the Laplace transform of integrate t to 0 te ^2t sin 2t dt

A: Given  : f(t) = t e2t sin2t To Find : laplace transformation Lt e2t sin2t

Q: Solve for the Laplace transform of et sint cost cos 2t cos 4t 7+4s+20 82-4+20 -4+68 4s+8

A:

Q: 2. Determine the Laplace transform of the given function using the Table coshbt te3t sin2 t

A:

Q: Laplace transform of sin(5t)u(t) is

A:

Q: Solve for the laplace transform of e^(at) cos bt using using the integral formula for laplace…

A:

Q: y' = 8x x(0) = 1 %3D x' = 2y y(0) = 0 %3D

A:

Q: 25. а. Apply Fourier transform to solve: ди for 0 < x, t 20 Under the conditions,

A: Given,              ∂u∂t=∂2u∂x2,  for  0≤x, t≥0           (1)Under the conditions,…

Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

A:

Q: VE cos(3f). find the Laplace transform of %3D

A: Laplace transformation is a method used for obtaining the solution of a complex differential…

Q: sin(2t) cos(2t)

A:

Q: Show that (a) L-1 = sin(at) - tcos(at) %3D (s²+a²)²) (where L indicates imverse Laplace transform)…

A: L-11s2+a22=12a2sin(at)-12a2tcos(at)

Q: Starting from the definition of the Laplace transform, calculate: a) L{(cosh(2t)}

A:

Q: What is the Laplace transform of 8'? 1 se sin s Cos s

A:

Q: Using Laplace Transform, solve the following initial value problem Зу' - 4y — sin 2t У) --

A:

Q: Solve Laplace Transform to obtain the solution of Differential Equations.Calculate each of the given…

A: Given:       ft=t2sin2t Apply laplace transform:        Lft=Lt2sin2t    Use laplace transform table:…

Q: Solve for the Laplace transform of e2t sin t cost cos 2t cos 4t

A:

Q: 1: A :Find Laplace Transform of f(t) = sin²t By Rule.

A:

Q: 9. Solve the IVP using Laplace transform: x' – x = 2cos5t, with x (0) = = 0.

A: Given equn isx'-x=2 cos 5t with x0=0taking both the side laplace transformation we get…

Q: Laplace solves the Initial Value Problem Find by transform.

A:

Q: 9. Find the mverse laplace transform of system function HS) = for 3 cases of ROCs when- s45s+6 (1)…

A: Consider the given function. Hs=1s2+5s+6 Find the factor of the denominator.…

Q: Solve for the laplace transform of e^(at) cos bt using using the integral formula for laplace…

A: The solution is given as

Q: Explain in your words how the Laplace transform is applied to solve a system of linear deferential…

A: The Laplace transform is an integral transform. The Laplace transform is mostly useful in solving…

Q: 5. * + 9x = cos 2t

A:

Q: 2) Solve the difference equation using z-transform yk+2 - 3 yk+1 + 2 yk = 0, with yo = 0, y, = 1.…

A: Since you have asked multiple question, we will solve the first question for you.  If you want any…

Q: Solve for the inverse Laplace transform of O 4cos at - 3 sin at 4 sin at – 3 cos at 3cos at - 4 sin…

A: It is known that: L-1a·fs+b·gs=a·L-1fs+b·L-1gsL-1ss2+a2=cosatL-1as2+a2=sin(at)