6. use Lapiace Transform to solve the lmitial valwe problem: y" +y = hlt) , ylo) = 2, y'lo) =0 where -4t 18TT, Olt L2H ht) o,

Q: 1. Find the laplace transform of sin(t)sin(2t) sin(3t), using est f(t)dt. F 1-4 3 1 r are. ².2.

A: As per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: Use the Laplace Transform to solve the given intitial value problem.

A:

Q: 2. Use Laplace transform to solve y" + y = 8(t – 27) cos(t) y(0) = 0, y(0) = 1

A:

Q: By using Laplace transform to solve the IVP: y" - 4y' +9y=t, with y(0) = 0 and y'(0) = 1 Then Y(s)…

A: Given IVP is  y"-4y'+9y=t ......(1) y(0)=0,y'(0)=1 .....(2) We fin Y(s).

Q: b) Using Laplace transform, solve the system UTM UTM dr dt -y = 1, UTMUTM dt dy given that r(0) =-1…

A:

Q: 59. By the transform method, solve Utt = Urx +h, 0 0, h = constant, Ut (x, 0) = 0, 0 0. u (x, 0) =…

A: We use Laplace transformation method to solve the given partial differential equation. Also use…

Q: Use the Laplace transform to solve the intial value problem. y′′+ 2y′+ y = −25e4t with y(0) = 1 and…

A:

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

A:

Q: 3. Use Laplace transform to solve the IVP y" + 9y = e', y(0) = 0, y'(0) = 0. %3D %3D

A: Laplace transferom, solve the intial value problem

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: 2. Use the Laplace transform to solve the given IVP: y"+4y' = 8(t - 1); y(0) = 0, y' (0) = 1 01:0…

A:

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

A:

Q: 5. Given that L{ sin VE} = 1/2s T /se-/4. determine the Laplace transform of (1/Vecos vt. %3D

A:

Q: Solve the following IVP using Laplace Transform. (i) y′′−4y′=e^(3t), y(0)=0, y′(0)=0 (ii)…

A: given Initial Value Problem is, (i) y′′−4y′=e^(3t), y(0)=0, y′(0)=0 (ii) y′′+3y′+2y=e^(-t), y(0)=0…

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

A:

Q: What is the value A 4B for Y(a)= which is Laplace transform of the solution of initial value 16…

A:

Q: Solve the following DE using Laplace Transform y" + 2y + y = 0, y(0) = -1, (0) = 1

A:

Q: Solve the IVPS by the Laplace transform. 1. y' + 5.2y = 19.4 sin 21, y(0) = 0

A:

Q: 2. Use the Laplace Transform to solve the following system x'= x-5y, y'=-5x+y, x(0)=1, y(0)=1.

A:

Q: By taking the Laplace transform Y(r, s) of y(a, t), solve the boundary value problem for a >0 and t…

A:

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

A:

Q: Solve the following IVP fu (t) ÿ+4ỷ + 4y = u(t), y(0) = 0, y(0) = 1 %3D by means of Laplace…

A: Here we are given an initial value problem.We have to solve it using laplace transform.

Q: Solve the IVP using Laplace Transform y" = y + 2y, y(0) = -2, y (0) = 3.

A:

Q: Solve the DE using Laplace transform. y" – by' + 13y = 0, y(0) = 0, y'(0) = -3

A:

Q: 1 Prove that L(sinh t) %3D (s2–1)

A:

Q: Solve the following IVP (without Laplace Transform): d'y , dy - 2y = 6 cos 2t + 2 sin 2t, y (0) =…

A: Solution: Given ivp is

Q: Compute the Laplace transform of integrate t to 0 te ^2t sin 2t dt

A: Given  : f(t) = t e2t sin2t To Find : laplace transformation Lt e2t sin2t

Q: Solve the following IVP using Laplace Transform. (1) y"-4y'=e^(3t), y(0)=0, y'(0)=0

A: The given linear differential equation is y"-4y'=e3t, y0=0, y'0=0

Q: b) Use Laplace transform to solve d?y dy + 2+y = te-t with y(0) = 1, y'(0) = -2 dt dt2

A: Inverse Laplace Transform

Q: What is the value of the inverse Laplace transform given by L 2s+1 8 J s2 +2s +3 O a. e-t (2…

A: Some Laplace inverse transform formulas: L-1(s-a)(s-a)2+b2=eatcosbtL-1b(s-a)2+b2=eatsinbt

Q: y" - 2 y' + 2y = 4 cos 2t + 2 sin 2t , y (0) = 1 , y' (0) = 1 %3D

A:

Q: Use the laplace transform to solve y'' + 4y' + 5y = S(t-2pi), y(0)=0, y'(0) = 0

A:

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

A:

Q: 35) dy - 4=1, Jco)=o

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

Q: Solve the following Euler type DE using Laplace transform:  y''+2ty'-4y=1 where y(0)=0 and y'(0)=0

A:

Q: 5. Laplaceovou transformáciou riešte rovnicu y" + 4y' + 3y = 8e', y(0+) = y'(0+) = 0.

A:

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

A:

Q: 15) Use Laplace transforms to solve y" +16y=8(t-2n), y(0) = 0, y'(0) = 0.

A:

Q: By using Laplace transform to solve y +y = tet with y (0) = -2, what would the particular solution…

A:

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

A:

Q: Take the Laplace Transform of the IVP (dy/dt) - y = 2cos(kt), y(0)=−9

A: Since in a given IVP it is mention that ''take the Laplace Transform'', therefore, we take only the…

Q: ди ди Solve the following PDE by using Laplace transform: ax %3D at ди x > 0,t > 0 with boundary and…

A:

Q: Solve the Laplace transform of the following: -3t. ii) y" + 4y" = -6y' + y – tet; y(0) = 0 and y'(0)…

A:

Q: 11 Calculate the line integral f Gy)ds for the given junc rion and path xiyl=xy KHt)=<3+,2t=-37 for

A: r(t)=&lt;3t,2t-3&gt;=&lt;0,-3&gt;+t&lt;3,2&gt; x(t)=3t  and y(t)=2t-3 ds=32+22dt=13dt 0≤t≤1

Q: 2. Solve using Laplace transform for y( y" + 4y' + 6y = 1- e-t, y(0) = 0

A: Given,          y''+4y'+6y=1-e-t, y(0)=0, y'(0)=0

Q: a) Sojlve the initial vajlue problem using Laplace transform UTM y + 2y = 26 sin 3t, y(0) = 3. UTM…

A:

Q: Solve the following IVP using Laplace Transform. (i) y′′−4y′=e^(3t), y(0)=0, y′(0)=0

A: Given IVP is y''-4y'=e3t, y0=0, y'0=0 Taking Laplace transform both sides…

Q: By using Laplace transform to solve y + y = cosht y (0) = 0, what would the particular solution be?…

A: the given equation is y'+y=cosh t  y(0)=0 taking Laplace of the given transform Ly'+y=Lcosh t…

Q: Solve the following IVP using Laplace Transform.  (ii) y′′−6y′+15y=2sin(3t), y(0)=−1, y′(0)=−4

A: Given differential equation is y''−6y'+15y=2sin3t and y0=−1 and y'0=−4 Take Laplace transform of…

Q: Solve the following DE using Laplace Transform y" + 2y' + y = 0, y(0) = -1, y(0) = 1

A: