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

Q: 13s 6+75 (s2-4)(s2+9)

A:

Q: Find the Laplace transform

A:

Q: L{t + et} =+ I. L{t + e3t} = = 1 %3D II. S-3 52 5-3 L{t + e*} =+ L{t + e#} = - III. IV. S+3 52 543

A:

Q: O Prove that Q(Vationalnumber bers)is negrigibleset

A: This follows easily from the definition of a negligible set. We recall the definition and present…

Q: 8s – 18 Find the inverse Laplace transformf(t) = L¯' {F(s)} of the function F(s) : s2 – 4s + 20

A: Consider the provided the question,

Q: 3.) f(t) = ½ (4-3) ² u(1-3)

A: Laplace transform of the function

Q: If L{f"(t)} = arctan ), f(0) = 2 and f'(0) = 1, find L{f(t)}. %3D

A: Given - If ℒf''t = arctan12 , f0 = 2 and f'0 = 1  To find - ℒft       Formula used - ℒfnt = snFs -…

Q: Problem 5 Using Laplace transform, solve y" - 4y + 7y = 0 y(0) = 3, y'(0) = 7

A:

Q: f (t) = e(-3t) sin(2t) cos(3t) cosh(t)

A:

Q: y"+ 5y' + 4y = 0 at y(0) = 1 and y'(0) = 0

A:

Q: Solve the inverse Laplace transform: 2s-4 s2+8s+13

A:

Q: f(t) = t5et 120 А. (s-4)6 24 C. (s-5)6 120 В. (s-4)5 24 D. (s-5)5

A:

Q: 2s2+5s-4 Find the inverse transform: F(s) s3+s2-2s A. 2 – et – 2e-2t C. 1+ 2et – e-2t B. 2 + et –…

A:

Q: f(t) = t2 cos 2t.

A:

Q: f(t) = e-2tsin²tcos²t

A:

Q: f(t)=cos(at). f (t) = 2cos(3t). f(t)=1-cos(wt) f(t)= 4t · -f(t)=e.

A: Given,     1.  f(t)=cos(at)

Q: 27-12 s L-1 (s+4)(s²+9)

A:

Q: y" + 3y - 4y = 6e²t-3, y(1.5) = 4, y'(1.5) = 5

A:

Q: -t cos(3t

A: To solve this problem, we  use the  result of laplace transformation.

Q: Find the Laplace transform

A:

Q: 4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) =…

A:

Q: f (t) 7t2 te-4t

A:

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

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: †3 – 12 +5t + 2

A: Laplace transformation of polynomial

Q: cos 4t-cos 2t 3. f(t) = t

A: