d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

Q: Example 7.5 Determine the Inverse Laplace Transform of the following expressions using Partial…

A: We use the table of Laplace transform to solve the given question.

Q: use the laplace transform to solve

A: Hi! As per norm we will be answering only the first question since both of the solutions are long.…

Q: 1 F(s) = (s - 2)(s - 4)(s -8)

A: Given the expression of the inverse Laplace expression is: F(s)=1(s-2)(s-4)(s-8) Use partial…

Q: a k 2 + k² S 2 + k² k

A:

Q: f(t) = e-2tsin²tcos²t

A:

Q: 4. Solve the initial value problem: y" + 3y' – 10y = 0, y(0) = 1, y'(0) = 0 -

A:

Q: F(s) = (8-2)e-* 8²-48 +3

A:

Q: x"(t) – 4x'(t) + 4x(t) = 4e2t; x(0) = -1,x'(0) = -4

A:

Q: on the function fcs) 35 - 17 s- 65+25 %3D

A: Inverse Laplace transform of function is : 12e3t(6cos4t-sin4t

Q: Solve the laplace transform 3x-6x= Sin 2t %3D given when t=0

A: Use the laplace transformation table and derivative formula

Q: 50 (s² + 15s + 2) 25s2 + 202s + 25

A:

Q: L{t – e-3t} = + s-3 L{t – e-3t} = =-- I. II. s-3 L{t – e-3t} = +3 L{t – e-3t} = III. IV. %3D s+3

A: We know the Laplace transforms Ltn=n!sn+1, s>0 L ea t =1s-a, s>a Now, Lt-e-3t=Lt-Le-3t L t…

Q: 3. F(s) = = 3s+2 (s-4) (s+1)(s-3) 4. F(s) = 5s-2 s³+3s²+s

A:

Q: y" - 4y + 13y = sin(2t) y(0) = y'(0) = 0

A: We have to solve the differential equation  by Laplace transformation.

Q: 0 9. f(t)=t-n 0 if t 2π

A:

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

A:

Q: FIND THE INVERSE LAPLACE TRANSFORM

A:

Q: Find L (t*ett)

A: You asked to find inverse Laplace transform.but your image is for Laplace transform.

Q: y"+ 6y'+ Sy -3t -st 1 - е se / у (о)= qў(o)=o

A: The differential equation is given by:  y''+6y'+8y=e-3t-e-5t      ,y(0)=0,y'(0)=0 We have to solve…

Q: Find L-1 (24) 3 2s-4

A: Answer

Q: f(t) = t²sinh3t

A:

Q: Write the function in terms of unit step functions. Find the Laplace transform of the given…

A: Laplace transform of the function

Q: y" – 4y' + 3y = 6t – 8 ; y(0) = 0, y'(0) = 0 - -

A:

Q: 3 cos(wt - a), where w and a are constants

A: We find the Laplace transform

Q: 1. F(s) = S-6 s²+4s+5 2. F(s) = 3s²+5s-4 54

A:

Q: Solve the shifted data IVP by the Laplace transform. Show the details.

A: We have given a initial value problem, y''-2y'-3y=0 with initial conditions y4=-3, y'4=-17 This is…

Q: Considering: { y"(t) + ty'(t) + ky(t) = 0 y(0) = v (0) = t0, k is a positive even number. Find a…

A: The Laplace Transform of an IVP , y''(t)+Ay'(t)+By(t)=f(t) y(0)=a and y'(0)=b is given by,…