69. (a) Use the Laplace transform to solve the heat conduction problem Ut = KUrx; 0 < x < 0, t > 0, и (х, 0) — 0, х > 0, u (0, t) = f (t), u (x, t) → 0 as %3D x → 0, t > 0. %3D

Q: 3. L{y"' + y' + 2y = sin 3t} ; when y(0) = 0, y'(0) = 0, y"(0) = 0

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Q: 9. Use the method of Laplace transform to solve the initial value problem y/" + B*y = (a² + 3?)eat,…

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Q: Use the Laplace transform to solve the given initial-value problem. y'' + y = delta(t − 6pi) +…

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Q: 2b. Determine the solution of the following problem using the concept of derivative and integral…

A: The given problem is to find the Laplace transform of the given integral term function.

Q: Use the Laplace transform to solve the given initial-value problem. y'' + 8y' + 41y = delta(t − pi)…

A: Given initial value problem, y''+8y'+41y=δt-π+δt-3π,y0=1, y'0=0 Solve this problem using Laplace…

Q: Use Laplace Transform to solve the initial value problem y' - 2y +2y=cos t y(0) = 0; y'(0)=1 %3D

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Q: 7. Use the Laplace Transform to solve the IVP y +2y - y -2y= sin(3t) ,y(0) = 0, y'(0) = 0, y'(0) =1

A: We have to use Laplace Transform to solve IVP.

Q: 1. Use the Laplace transform to solve the given initial-value problem. (1, 0st< sint, t2 y" + y =…

A: Given : The initial value problem   y''+y=f(t) , y(0)=1, y'(0)=0, where   f (t) = 1 ,         0…

Q: 1. A) Evaluate the integral fe"(1+t sinf)dt by using Laplace transform definition and properties of…

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Q: Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y' (0) = 3. %3D (a) Use the Laplace…

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Q: 64. Use the finite Fourier cosine transform to solve the heat conduction problem t> 0, 0 0, where…

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Q: 5. Use Laplace transforms to solve the initial value problem y" + 3y - 10y = 13(1-cos(t)), y(0) = 1,…

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Q: 15 Solve the IVP using Laplace transforms. x'(t) = t, x(0) - 4

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Q: Determine the constants a, p, yo and y'o so that Y(s) = Bs + C (s + D)² is the Laplace transform of…

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Q: Q5. Find the Laplace Transform of the funetions x(t) and yıt), which satisfy the coupled first…

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Q: 3. Using Laplace Transform Solve d'y dy = sint, given that y =! dy =0 when t=0 +2 - 3y dr? dt dt

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

Q: 7. A damping system with a negligibly small spring constant is modelled by x' +bx' = a e1 with…

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Q: 6. Use Laplace transforms to solve the initial value problem, 4t, 0<t<1 y' +2y = f(t), y(0) = 0,…

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Q: 4. Use Laplace transform to solve the fowowing Initial -value problem : y" *y =hlt),ylo)=1,y'l=2…

A: In the question it is asked to calculate the initial-value problem using Laplace transform.

Q: 17) By applying the Laplace transform to solve the integral equation y(t) – at? = b | sin(bt –…

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Q: TM a) Solve the initial value problem using Laplace transform UTM UTM UTM y + 2y = 26 sin 3t, y(0) =…

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Q: Use the Laplace transform to solve the given initial-value problem. y'' − y' = et cos t,    y(0) =…

A: Given :y'' − y' = et cos ty(0)=0, y'(0)=0

Q: 2. Use Laplace transform to solve with y(0) = 1 and y'(0) = 0. y" + 2y' + 2y = 8(t = π)

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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: 10. Use the method of Laplace transform to solve the initial value problem y" – 2ay + (a? + B²)y =…

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Q: 8. Use the method of Laplace transform to solve the initial value problem y" – 20y + a?y = (a –…

A:

Q: Use the Laplace transform to solve the given initial-value problem. y"+y= (t-극) + 이t-), y(0)= 0,…

A: The Laplace transform is an integral transform that converts a function of a real variable t to a…

Q: Use Laplace transform to solve the given initial value problem. Graph your solution on interval (0,…

A: Use laplace transform to solve the given initial vlue problem.y''+y=∑k=1∞δt-kπ,   y0=0, y'0=1And to…

Q: Use the Laplace transform to solve the given initial-value problem. y(t) 11 y""+ 2y" - y' - 2y =…

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Q: 25. Solve the BVP using the Laplace transform method PDE: un = c¯Ux 0<x< ∞, 0st<∞ ВС: и(0, г) — 0…

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Q: 2. By Laplace transform, solve the D.E. y' + 2y = 3te-2t, y(0) = 4.

A: Using Laplace transformation,

Q: By using Laplace transform to solve y"-y e' with y (0) = 1 and y (0) = 0 ,what would the particular…

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Q: Use the Laplace transform to solve the given initial value problem. y" - 2y' + 2y = cos t; y(0) = 1,…

A: The differential equation is given as : y''-2y'+2y=cos ty(0)=1y'(0)=0 The objective is to find the…

Q: Use Laplace transform to solve the initial value problem y" – 2y' +y = e", y(0) = 0, y (0) = 0. %3D

A: Given problem :

Q: 1. Use Laplace transform to solve y" + 3y + 2y = u(t – 2) y(0) = 0, y'(0) = 1

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Q: 7. Use the method of Laplace transform to solve the initial value problem y" – (a + B)y' + aBy = (a…

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

A: The given differential equation is: y''+4π2y=2πδ(t-1) ;              y(0)=0,  y'(0)=0

Q: 1. Use the Laplace transform to solve the following IVP: y"-2y' = e²" cost, y(0) = 0, y'(0) = 0

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Q: 3. Solve the Initial Value Problem by the Laplace transform. y" – 12y' + 5y = 15cos(t), y(0) = 3.2,…

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Q: 13. Use the Laplace transform to solve the following differential eguation y" + 4y/-5y 10 with y(0)…

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Q: 2. Use Laplace transform to solve with y(0) = y" + 4y = = 8(t)- 8(t - 2π) 0 and y' (0) = 0.

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Q: Use the Laplace transform to solve the given initial-value problem. y'' + 2y' + y = 0,  y(0) = 1,…

A: A detailed solution is given below.

Q: 2. Use the Laplace transform to solve the following initial value problem: y" + 2y' + 10y = cos(2t);…

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Q: 10. Use the method of Laplace transform to solve the initial value problem y" – 2ay + (a? +B²)y = 0,…

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Q: 4)Use Laplace transform to solve y +2y +2y=e", y(0) = 2, y'(0) = -1

A: Given y"+2y'+2y=e-t , y0=2 , y'0=-1 Ly"=s2Ly-sy0-y'0 Ly'=s Ly-y0 Le-t=1s+1 Now…

Q: Use the Laplace transform to solve the given initial-value problem. у" + у %3D 8(t - бл), у(0) —- 0,…

A: We will find out the required solution using Laplace transform method.

Q: 2. Use Laplace transform to solve | cos(4t), 0T y" + 16y = ; y(0) = 0, y'(0) = 1.

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Q: 2. By Laplace transform solve the boundary value problem 00 %3D u(0, t) =0, u(1,1)= 0, 1 >0 Subject…

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Q: y" +y = 8(t- 2m), y(0) = 0, y'(0) = 1 %3D

A: