Topic: Laplace Transform   Please solve Nos. 6 and 7

Q: y Ct) = 5e - 2t Cos 67 fCt) = 3c 4t C1- 3t + 2t 2) -4t (1- 3t + 2t²)

A:

Q: Use the Laplace transform to solve the initial value problem y'" + y' – 2y = 2e*, y(0) - - 1, y'(0)…

A:

Q: g(t) = 10rect [²(t+³)] ej²¹ 5 ej²nfot j2πfot

A: What is Fourier Transformation: A Fourier transform (FT) is a mathematical transformation that…

Q: 8. y" +9y = 20e y(0); y' ||

A:

Q: Consider the following IVP: y"-3y'+2y = e*; y(0) = 0, y'(0) = 0 Find the general solution.

A: We solve the given DE  y"-3y'+2y=e3t.......(1) y(0)=y'(0)=0......(2)

Q: 1. 2 (t+2 cos 2t)²-2 cos²2t 2 sint (e²t + 4e¯¹ + sin t)

A:

Q: f(d) = e-2d d4

A:

Q: Let A = -127 0 -8 4 0 and 6- = 36 7 Define the linear transformation T: R2 → R³ by T(x) = Ar. Find a…

A:

Q: co sh?Ł

A: As we know,    cosht = exp(t)+exp(-t)2                  and               Laplace transform of ept =…

Q: 2ct-3) cos Cも-3) yct) = sin 2t cos 3t

A:

Q: Solve Laplace Transform of staircase problem

A: Formulae to be used: Laplace of function f(t) is: L{f(t)}=∫0∞f(t)e-stdt. 11-x=1+x+x2+x3+...

Q: ZA'B'C' is the image of LABC following the reflec- tion of ZABC across line (. If mZA'B'C'= + 20 and…

A: Given: m∠A'B'C'=x5+20, m∠ABC=x2+5 We know that when we take reflection of a triangle across any line…

Q: Question 1.i.) A truncated sine wave { sin5x, -T <x <T y = f(x) = 0, otherwise

A:

Q: 7s2 – 3s + 26 F(s) (8 – 1)(s² + 9)

A: Explanation of the solution is given below...

Q: Obtain the F(s) of the following f(t) 1. f(t) = } (-1 0st<1 ={'1 t21

A: we have given the function f(t)=-1  , 0≤t&lt;1  1  ,    t≥1 we have to find the Laplace…

Q: Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 13 5r…

A:

Q: Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0

A:

Q: Solve the equation subject to the given conditions. d'y dy dx² dx 6y=4, y(0)=3, y'(0)=2

A:

Q: Instruction: Answer the following: I. Prove: S L{cos at} = 2+²

A:

Q: Lft etc ezt coth 3t dt 2t 8

A:

Q: Exercise 3: Find the Laplace transform of f(t) = cos (t -).

A:

Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1 Find the general solution. A y (1) =…

A:

Q: 8. Solve using Laplace transform: y" + 2y – 3y = 8e¬t + 8 (t – ), y(0) = 3, y' (0) = –5.

A:

Q: Describe the connection of Chebyshev to Fourier.

A:

Q: Give 5 simple or basic examples of Laplace Transforms with solution.

A: First example: We have a formula Ltn=n!sn+1 So, one example is for n=2: Lt2=2!s2+1=2s3 Hence,…

Q: Using second-shifting theorem find, F(s) where f(t) = e-4t sin 3t

A:

Q: Find F(2). 5sinh (3t) + 4cosh (3t) round off to 1 decimal place. Answer: -4.6

A:

Q: Solve the Fourier Transform of the function using the different Fourier Transform properties and…

A:

Q: If a function is Fourier transformaboe, is there any guarantee that the function will be Laplace…

A:

Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

Q: (8) 5 2.

A:

Q: According to Kirchoff's voltage law, the sum of the voltage drops across these elements is equal to…

A:

Q: Solve all the Laplace transform in the image attach

A: Laplace transferom of the pice wise function, and Laplace transferom of divisibility by t theorem