Q.5 (a) Using Laplace transform solve: dzy - 49 + 3y = e2t given that dt2 y(0) = 2 and y'(0) = –1. (b) Find the Inverse Laplace Transform: (s+8) I. (s²+4s+5) II. 1 s(s-2)

Q: 2s +3 Find the Inverse Laplace Transform of F (s) s²+4s+ 13 A f (t) = 2sin3t – -cos3t 3 B f (t) = e'…

A: Use Laplace table.

Q: How do you solve this problem?

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Q: 2s- 1 What is the value of the inverse Laplace transform given by g2 +2s +3 O a. et (2 cos(/2t) –…

A: Let's find.

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Q: Use the Laplace transform to solve the given initial-value problem.   y'' + y = 2sin(2t), y(0) = 6,…

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

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Q: Use laplace transform to solve the initial value problem; a) y'+y=alpha(t-1),y(0)=2

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Q: Suppose an undamped forced spring mass system is driven by the equation + 9x = f(t), dt where the…

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Q: a) Solve the initial value problem using Laplace transform I UTM UTM 26 sin 3t, y(0) = 3. UTM

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Q: kado/4 Find the Laplace transform for -4 f() = e'sin2t + e cost s + 1 2 s+1 s + 2s + 5 s- 2s + 2 (s-…

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Q: 3s +5 Let X(s) = be the Laplace Transform of a signal x(t). Then, x(0+) is %3D s + 10s + 21

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Q: 4s²-5s+6 (s+1)(s²+4) 2- Inverse Laplace transform for a) f(t) = 3et+ cos2t - 3 sin 2t b) f(t) = et +…

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Q: Use the Laplace transform to solve the given initial-value problem. y" - 3y' = 4e²t - 2e-t, y(0) =…

A: I have solved step by step in detail....go through the solution

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

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

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Q: 1. A) Evaluate the integral [e(1+t sint)dt by using Laplace transform definition and -st properties…

A: The solution is given as

Q: Use laplace transform to solve the initial value problem; a) y''+y=alpha(t-1/2pi)+alpha(t-3/2pi),…

A: Given                     y''+y=α(t-1/2π)+α(t-3/2π),and      y(0)=0,        y'(0)=0…

Q: Use laplace transform to solve the initial value problem; a) y''+2y'=gamma(t-1),y(0)=0,y'(0)=0

A: We have to find Laplace transform of  y''+2y'=gamma(t-1),y(0)=0,y'(0)=0

Q: 5. Compute L-1{F (s)} where 3s 5 F (s) (s2 +4)2 6. Use the Laplace Transform to solve the IVP Find y…

A: 1) To determine  f(t) such that its Laplace transform is the given F(s), and 2)  solve the initial…

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: 2s2 +13s+6 Find the inverse Laplace transform of H(s) = (s+2)2(s-1) assuming that a) h(t) is causal…

A: We will find out the required inverse Laplace transform of H(s)

Q: How do I solve for the third order y''' - 4y''-11y' + 30y = 4e^8t + t^2 using the method of 1.…

A: repost the question for other method separately

Q: solve for Y(s), the Laplace transform of the solution y(t): y'' +6y'+5y=te^t  where y(0)=2 and…

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Q: 2) Using Laplace Transforms, solve the following initial value problem y" - 4y' - 5y = cosh(2t),…

A: Solution

Q: 2s +3 Find the Inverse Laplace Transform of F (s) s2+4s + 13 A f(1) = e-"(cos31 – sin31) 2 (B) f(t)…

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

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Q: Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace…

A: Given differential equation is  y''+25=cos(5t) with initial conditions y(0)=3 , y'(0)=2 we have to…

Q: 8 3 Find the Inverse Laplace Transform of- + 3s2+ 12 s2– 49 3 4 A) - sin2t + -cosh ( 7t) 7 3 4 –…

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Q: -2sin4t Determine the Laplace transform of the equation f (x) = 2 e´ 10 A s²+4s+20 8 B s²+4s+ 20 20…

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Q: у" + 6у' + 10у %3D 1, У (0) %3D —1, y'(0) = 2

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Q: QUESTION 3B Given two differential equations: dx dt + 4% + 6y = 0 dy dt 5 + 2 + 6x = 0 dy dt dt…

A: Given:           dxdt+4dydt+6y=0.....(1) and 5dxdt+2dydt+6x=0.....(2) with initial conditions x0=3,…

Q: (b) 2s2 -4 Find the inverse Laplace transform of the function F(s) = (s+1)(s-2)(s-3) by using…

A: Solve the problem with the help of partial fraction

Q: 2s+1 Determine the Inverse Laplace Transform of: L{; (s²+4s+4)(s2-4)*

A: Let us assume L{f(t)}=F(s) Laplace transform of some unknown function f(t) is given…

Q: Determine the constants a, p, yo and y'o so that 3S +3 Y(s) = (s + 2)² is the Laplace transform of…

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Q: 3. Using Laplace transform, find the solution of conditions y(0)=3 & y'(0)=1. d²y dt² +2y = cos 2t,…

A: Given d2ydt2+2y=cos2t with initial condition y0=3, y'0=1

Q: Solve the following initial value problem (IVP) of y" – 3y - 10y = 2 where y(0) = 2 and y (0) = -1.…

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

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Q: 25. а. Apply Fourier transform to solve: ди for 0 < x, t 20 Under the conditions,

A: Given,              ∂u∂t=∂2u∂x2,  for  0≤x, t≥0           (1)Under the conditions,…

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

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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: e-cos3t Using Integrals of Laplace transform L S Lle - cos3r]ax a. bS Lle?r-cosat]ds -cas3r]ds d.…

A: By the using of laplace transform formula table

Q: 1. Use Laplace Transform to solve the initial value problem. Show your complete solution. y" - 3y +…

A: Solution

Q: 5 The inverse Laplace transform of the function sin(2t) (A) 1 – 2 sinh(2t) (B) t- 2 sin(2t) (C) t- 2…

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Q: 2s+4 What is the value of the inverse Laplace transform given byL 82 +2s + 3

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

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Q: Solve the initial value problem using Laplace Transform Method y" - 4y = sin 2t y0) = 3, y'(0) = 0…

A: The given initial value problem is  y''-4y=sin 2t   , y(0)=3,  y'(0)=0 As we know…

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

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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: Q9. (a) i. Find Fourier transform off (x) = x e¯*,0< x < ∞. ii. Find the inverse Fourier sine…

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