5. L-1(++: = e-2x + cos 2x +sin v3x V3 = e s+2 s2+4 s2+3/

Q: L-¹ s+2 2s²+4s+ 7

A:

Q: -7 s(s+3) 2

A: Given: L-1-7SS+72

Q: 3. L(x* + x² – 7) -7s*+2s² +24 %3D | s5

A:

Q: 4. Find L'{ -}. Give table number. 3-5S

A: We have to find L-123-5swe are going to use the formulaL-11s-a=eat ——(*)

Q: 2 5) L-1 (s – 2)³. s+2 6) L-1, ls² + 4s + 13)

A:

Q: a) Solve the initial value problem using Laplace transform IMUTM UTM UTM IM UTM TM UTML

A: First we take Laplace transform of given differential equation and solve.Then solve for inverse…

Q: • A • P

A:

Q: Determine the Laplace Transform of sin³3t

A:

Q: Prove that (1, 2) (1,(1), 2, 3).

A: We know, if A and B are two sets then, A is subset of B  if every element in A is also in B.

Q: Find the inverse 2-Transforrm of log(z f log 241 by Power senies method and by division method

A:

Q: L{5t? + 12t + 25}

A:

Q: From Leibnitz theorem °C=

A:

Q: f(t) = e-3t sin(4t).

A: Introduction: Laplace transform is named in honour of the great French mathematician, Pierre Simon…

Q: 3. State and explain the Convolution Theorem for Laplace transform

A: To prove: State and explain the convolution theorem for Laplace transform.

Q: +23

A:

Q: transform is Use Python to find a function whose Laplace 2(s - 1)e-3⁹ s² - 2s + 2

A: import sympy as sp# Define the Laplace domain variables = sp.symbols('s')# Define the Laplace…

Q: x* 2 2 xzəz = (+)1-7 o + 12 s-2

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: Solve the following Laplace Transform of Algebraic Expression: 4. Find the L te2t ?

A:

Q: Find inverse Laplace by residue theory 2. XeS+(て-2x。) s- 25+5

A: Find the Laplace inverse transform by residue theory L-1x0s+x1-2x0s2-2s+5

Q: Determine the Laplace Transform of est cos 5t .

A:

Q: Find the inverse Laplace transform of each function: -4s a) F(s) = -5/2.

A: We find out the Laplace inverse transform .

Q: 2 5) L |(s – 2)³J s+2 5) L-1 ls² + 4s + 135

A:

Q: Determine the Fourier transform of e cl, with ca positive number.

A:

Q: -3iw sin 5w 20e F(@) = %3D 3

A:

Q: 3s-16 3.) s2-24s+69

A:

Q: Use the definition of Laplace transform and Euler's formula to find the Laplace transform of cos t…

A: We use the definition of Laplace transform and Euler's formula to answer the given question.

Q: I the Fourier transform of f(t)= 3sin5t +4cosl %3D

A:

Q: Apply the definition of the Laplace transform to find sin bt.

A:

Q: t²e³t sin 2t 3t

A:

Q: 2s +3 Deter mine the inverse Laplace transform. of

A:

Q: Find the Laplace transform of sinhot. Recall that coshot = {sinhbt} = | [sinhbt} = {sinhbt} =…

A: