|17. f(1) = cos² 21 17. cos? 21 = (1+ cos 47); [s-1 +s/(s² + 16)].

Q: 10. Solve the following IVP using Fourier Transform: -00 0, u(x,0) = e, -0 <r < oo.

A: Given ut=uxx, -∞&lt;x&lt;∞, t&gt;0u(x,0)=e-x2, -∞&lt;x&lt;∞

Q: 3. f(t) = t°e^(-4t) 4. f(t) = (e^(10t)) sin(2t)

A:

Q: Solve the problem: y "- 4y=excosx ,   y (0) = 1, y '(0) = 2 a) without using Laplace transform; b)…

A: Consider the given information. (a) Use the undetermined coefficient to solve the equation. Write…

Q: SOLVE FOR INVERSE LAPLACE TRANSFORM 3s + 2 4s2 + 12s + 9

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The Laplace transform of L[2 sin 6t sin 3t] is 2s s2 + (3)2 s2 + (9)² s + (3)² s2 + (9)² | s2 + (3)²…

A:

Q: Solve the Laplace transform of; L-1 3s + 10 s² + 4s + 20/

A: Using the table of Laplace transformation, it can be written that:…

Q: 1 -s F(s) = e = -+ s2 e-3s

A:

Q: 1 Find the Inverse Laplace Transform of s2+2s + 10 A -e 'sin9t 3 -e-'sin3t 3 3t e"cost (D 3 "cos3t…

A:

Q: Solve the equation dy y ху-з dx II +

A: The given equation is of the bernoulli's equation form.

Q: 2(+-3) cos (t-3) y ct) : Sin 2t cos 34

A:

Q: By using Laplace transform to solve y - y = sin(2t) with y (0) = 1, what would the particular…

A: The solution is given as

Q: Problem 2 4s +3 (s – 1)°(s²+ 4) |

A:

Q: Consider the IVP y''-y'=-30e3tcos(t), with y(0)=1, y'(0)=-12. Take the Laplace transform of both…

A:

Q: SOLVE FOR INVERSE LAPLACE TRANSFORM 6s – 4 - s2 4s + 20

A:

Q: Find the Laplace transform of the following: 1. e3t cos 2t 2. sinh3 4t 3. te-lu(t – 1) 4. t cosh 2t

A: 1) Given:    e3tcos 2t      Applying Laplace transform       Lft=Le3tcos 2t Apply transform rule:…

Q: Determine the Laplace transform of e-5t sinh(6t) · е s+5 s2 – 10s–11 6. s2 – 10s-11 s+5 10

A:

Q: Example 5 : Using Laplace transform method, solve (D² +1)y = 6 cos 2t,t > 0 If y = 3, Dy = 1 when…

A: The given problem is to solve the given initial value problem with given initial conditions using…

Q: 2. e-4t sin (8t)

A:

Q: What is the inverse Laplace Transform of a function y(t) if after solving 32-s+3 Differential…

A: Given To determine inverse Laplace transform of a function y(t) Using inverse Laplace transform…

Q: The Laplace transform of L2 sin 6t sin 3t] is S - s + (3)² s2 + (9)2 S 2s + (9)* s2 + (9)² s² + (3)²…

A: Solution by using trigonometric identities and Laplace transform table as follows :

Q: Use Laplace transforms to solve the following initial value problem. х" + 4x%3D sin 5t, x(0) 3 0,…

A: The given problem is to solve the initial value problem using Laplace transform, we have to apply…

Q: QUESTION 10 The Laplace transform of t sin(3t) 6s (s² -9)? 6s (s²+9)? 6s

A:

Q: Solve for the Laplace transform of e2t sint cost cos 2t cos 4t 1 s-4s+20 s-4s+68 -4s+20

A:

Q: 04 Obtain the particular solution for: 2y" +2y= 2 sinx y(0)=0, y'(0)=1 (a) By using Laplace…

A: The solution is given below in the next step:

Q: Consider the IVP: y" - y' + 2y = 8sin(2t) - 8, with y(0) = -2, y'(0) = -4. Solve the IVP by using…

A: Given IVP is y''-y'+2y=8sin2t-8              (i) With y0=-2, y'0=-4 Taking Laplace transformation of…

Q: (sin³r} = {1-co52} and find the Laplace transform: S 1 2 -3²+2 S 1 2 O 1(1 1/1 S +4 +2

A: Given formula of sin^2 t is in terms of cos2t. For detailed solution, visit step 2.

Q: Find Lf" sin /6t-r'e"}

A: Please see below

Q: 1. Show that the function 2t et cos (et“) is not of exponential order, however its Laplace transform

A:

Q: Solve for the Laplace transform of et sint cost cos 2t cos 4t 7+4s+20 82-4+20 -4+68 4s+8

A:

Q: The inverse laplace transform of 3s2+4/s(s2+4) is A. 1+cos 2t B. 1+3cos 2t C. 1+2cos 2t D.1+3cos t

A:

Q: 3. e-9t cos(3t) + 5e-2t sin(3t)

A:

Q: * Find the inverse Laplace transform for-5 1 F(S) S + 25 5 sin(5t) 1 sin(5t) 1 s O 0 خیار 3 sin(5t)…

A:

Q: dy - 5y = e, a Yo = 1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the following DE using Laplace Transform Method. Show your complete solution y" -2 y' +2y = 4…

A:

Q: Find the Laplace Transform of e 2 cos3t + 5e 2 sin3t - s+2 + s2+9 15 A. g²+9 (s+2) + 15 (s2+4s) + 13…

A: To find the laplace transform of given function first we will use the linearity property of laplace…

Q: [2.] Solve the IVP yu+ 6y'+9y= e-*cos 2x COS2X t. Fed the Laolace transform

A:

Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

A:

Q: ) Solve the following initial value problem by using Laplace transform. y" + 4y = 4t + 12, y(0) = 4,…

A:

Q: The Laplace transform of L[2 sin 5t sin 4t is s+ (1)2 s2 + (9)2. 2s s2 +(1)2 s2 + (9)2 s2 + (1)2 s2…

A:

Q: -3s? + 2s +4l | (8² – 4s + 5)(s – 2) * 1. Calculate the inverse Laplace transform L-1

A: Inverse Laplace transferom of the function

Q: Use Laplace Transform to solve the given Initial Value Problem.  y''+9y=cos(3t)  y(0)=2 y'(0)=5

A:

Q: I find the Laplaa Transform ) f4): e" (3t*+ 1) - 5 sin at 5 sin 3t

A:

Q: The Laplace transform of t sin(3t)is : 30s2-54 (s2+9)3 12s-54 (s2+9)% 18s-54 (s2+9)2 12s2-54 (s?+9)?…

A: We find the last transform of t2sin(3t)

Q: 2. Find L{e3t cos 2t} using property of Laplace transform

A: We’ll answer the first question (Question number 2) since the exact one wasn’t specified. Please…

Q: ve an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in Figure…

A:

Q: 2. cos(2t) + 7 sin(3t)

A: we have used laplace property and table for this question.

Q: By using Laplace transform to solve y" + 4y + 8y = sint with y (0) = 1 and y' (0) = 0, what would be…

A:

Q: By using Laplace transform to solve y' +4y +8y = sint with y (0) = 1 and y (0) = 0, what would be…

A:

Q: Find the Laplace Transform ofe 2 cos3t + 5e21 sin3t s+2 15 A g2+9 s2+9 (s+ 2) + 15 в (s2+4s) + 13 15…

A: