1 s'+5s 5.) 5 L' s² +4s+6 6.)

Q: se-2s c) F(s) (3s+4)(s-1)

A:

Q: c. (D²5)y=x²-2; y(0) = 0; y'(0) = 2

A:

Q: 7.2 . 2 S 1 s – 2

A:

Q: F (s) = e4-3s (s+4)5/2

A:

Q: 6s L-1 (s² + 9)²

A: Apply the inverse transform rule that is if L-1Fs=ft  then L-1sFs=ddtft+f0  . The expression 6ss2+92…

Q: + dy-39 sin ax y co) y'o) =12

A: Laplace transferom for the differential equation

Q: s-1 s(s+ 1)² -1+et+2te-t 2+te-t-e-t O Option 1 Option 3 1+et-2te-t Option 2 -2+tet + et O Option 4

A:

Q: 3(s-4)e-5s F(s): %3D s2-8s+25

A:

Q: 3s2 + 5s + 1 (s)= (s2 + 15s + 34) %3D

A:

Q: (s) = 20 (s+3)(s² +8s+25) f(t)=2e-3t2e-4t cos3t- -

A: As per the guidelines I am answering only one question at a time.[1]

Q: S 2 S+S-20

A:

Q: 23. F(s) = 5s² + 34s + 53 (s+3)²(s+1)

A: We will partial fraction decomposition to separate the factors of denominator and then use inverse…

Q: f(1) = sin? (t + x) sin (t + ) = S1

A: Given:      ft=sin2t+π

Q: Solve for the Inverse Laplace of this equation

A:

Q: s+ 8 F(s) %3D s2 + 16s + 68

A:

Q: 3 cosh 5t 4 sinh 5t

A:

Q: 1) S-4 5²-85+ 10

A:

Q: Examples: find the inverse laplace F(s) = 2s2 + 5 s3 +6s? + 5s -12

A:

Q: 6 F(s) (s? –48+20)? cos 4t 3 -2t sin 4t 3 -2t O f (t) te 64 16 t e2t cos 4t 3 2t sin 4t 3 O f (t) 64…

A: Inverse Laplace property

Q: S-a (s-a)'tb2

A: Inverse Laplace transferom

Q: ₂ (91+₂²) - F(S)

A: Given: Fs=1s2+162. We have to find the inverse Laplace using convolution.

Q: I- 100 (s+10) (s+20)

A: Inverse Laplace transform

Q: s-1 Y(s) s2 +4s+5

A: Given that,

Q: 5s-2

A:

Q: Solve + 3y + 2 ,: y dx = x, given y (0) = 1. dx

A:

Q: y"+3y'+2y=t; y(0)=0, y'(0)=2

A:

Q: answer this inverse laplace

A: Apply Laplace inverse on both sides