4) Using Laplace transform to solve y" + 9y = cos³t, yco)=1, y'co)=5 Hint: ду Lr sinkt + Ktcoskt} 2KS = (3²+k²)²

Q: Q"+4Q'+4Q=2t Solve with Laplace transform

A: Using laplace transform to solve the problem.

Q: 1. f(t) = 5(e^-4t)[cos(10t)] A. (5s – 20) / (s^2 - 8s + 116) B. (s - 4) / (s^2 - 8s + 116) C. 50 /…

A: Laplace transferom of the function

Q: From Euler’s formula e^it= cos(t) + isin(t) show that a) cos(t)= 1/2(e^it+e^-it) then show…

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Q: Solve for the laplace transform x(t)= (cosh4t sin4t)/ (te6t)

A: The given function is x(t)=cosh 4t sin 4tt e6t=cosh 4t sin 4tte-6t

Q: Find ay dt + = -1 (+-√e ³ sin ¹ (2+) 1(5+2log +) 9

A: We will use the formula ddtmn=nm'-mn'n2

Q: 2. Reduce to an exact equation and solve it: dy_2xsin 2 y+(2siny)/x² dx 2x²cosx-(2cosy)/x (2x²ysin…

A: GIVEN: dydx=2xsin2y+(2 siny)/x22x2cosx-(2cosy)/x             (2x2y siny -x y3sinx)dx +(x3siny +x3 y…

Q: To find the Laplace transform of e^(6t)cos(at)you would substitute  into s/(a2+s2) which gives ?…

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Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=2.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: find dy/dx y = | Vx V 1 5) 1+x 20) y=Cof"| 1-x, 15) y = \tan /2x + 7

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Q: Solve equation using Laplace transform ÿ + 9y = 8 (t -) |sin(t), y(0) = 0, ý(0) = 0

A: Formulae:  1. Lf(t)δ(t-a)=e-asf(a) 2. Lf''(t)=s2F(s) - sf(0)-f'(0) 3. L-1e-asF(s)=H(t-a)f(t-a),…

Q: 6. Evaluate * у" + 9у 3 0; у(0) — 2 , у'(0) %3D 9 2cos3t + 9sin3t 2cos9t + sin9t А. В. 2cos3t +…

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Q: The equation x''+ x = sin t has a bounded solution. true or false ?

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Q: 0st<"/2 – "/2) tz"/2 Solve using Laplace transforms. y" –- 3y' - y = } y(0) = y'(0) = 0 cos(t SHOW…

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Q: 3. f(t) = [sin(2t)]^2 %3D

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Q: Confirm that the standard Fourier forward transform of the double-sided decaying exponential signal…

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Q: 8)find dy/dt for y=cos^2(3#t-1) # is actually pie or 3.14 etc I just don’t have the symbol on my…

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Q: 2. f(t) = -7(e^3t)[sinh(2t)] A. -14 / (s^2 – 6s + 5) B. (-7s + 21) / (s^2 – 6s + 5) C. -14 / (s^2 -…

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Q: Use Fourier cosine transform to solve y" – y = 3e-4 y' (0) = 0 lim y (x) = 0, as x → o0

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Q: Sole by Laplace Transform: y''-4y=4t-8e^(-3t);  y(0)=0, y'(0)=1

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Q: 7. Find the Inverse Laplace Transform of 3/ sqrt [(s - 2)^3] * A. (6/T) [ t^(1/2) e^2t] B. (6/T^1/2…

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Q: What is the Fourier transform of 8(x) dx F(k) = 100 = 2T -ikx 8(x) =?

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

Q: Use Laplace Transform to solue y' +zy y=4et %3D given ylo)"= 2 and y'lo). y'66)=-1 %3D

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Q: What is dy/dt of the given? Show both the simplified and unsumplified answer.

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Q: Find the Laplace transform of (e^ (2t)) sinh (4t) (-s^3 + 11s 2 1. (e^ (3t)) cos (5t). A. 56s + 196)…

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Q: Find Laplace transform of the function: f(1) = sin 21(et cosh 41+ cos(x + 1))+1(2 cos 31+1'e¹) 11.00

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Q: The inverse Laplace transform of F(s) = = -98 e 8² +18 2 is

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Q: use LaPlace transforms find solutions for dx/dt+3x=e^-2t, given that t=0 and x=5.

A: The objective of this question is to solve the given differential equation dx/dt + 3x = e^-2t using…

Q: 3 y = sin³ 2x

A: We have to use chain rule here.