. Utilizing Laplace transforms and matrix-vector formulation, solve the initial value problem yi = -2y2 + 5 sin t · u(t – 2T), y2 = -2y, with y,(0) = 0 and y2(0) = 1. The following partial fraction expansion might be useful in finding inverse Laplace transforms. As + B Cs + D – a² ' s² + w² 1 %3D (s² – a²)(s² + w²) ¯ s² where the coefficients A, B, C and D can be easily determined by considering s | = jw.

Q: For ut + aux = 0 (a) Write down an implicit difference method (backward Euler difference in both x…

A:

Q: How to solve this equation y''' - 8y" + 4y' +48= 4x2+1 using Laplace Transformation.

A: Converting the equation in Laplace transform:…

Q: 2²u at² ·x 20u = 0, əx² -∞0 0 the equation subject to the initial and boundary conditions: u(x,0) =…

A: Solution:- Given equation is homogeneous wave equation for infinite string

Q: Find the inverse Laplace Transform of: 11 5s 3 1 F(s) s2 + 3 s2 + 9' 5s – 7 s4

A: Use the formulas below to calculate the inverse Laplace transform.

Q: Using Laplace transform, solve the following simultaneous equations: y₁+3y1 - y2 u(t-1)et, Yo…

A: We solve given simultaneous equation by using Laplace transform.

Q: 3e-2t, where x(0) = *(0) = 0 Q2. Find the response of a system * + 5x + 6x = a. Obtain the transfer…

A:

Q: (a) Compute the integral 7² ſ tri(t)e¬j¤tdt [Hint: Fourier Transform.] use Fourier transform tables…

A: Since you have asked multiple question.As per Bartleby's rules I will answer only first question.If…

Q: 3) Compute the inverse Laplace Transform. e-3s Y(s)= s²+2s+2

A: (.). Given function is ,           If   , then

Q: Use a Fourier transform to solve the following initial value problem for the free Schrödinger…

A: Given: Let us consider the given ut=iuxx ; ux,0=e-x2

Q: Use Laplace transform technique to solve y+2y +2y=e"! y(0) = -3, y (0)= -3

A: Solution: The objective is to find the solution of the given differential equation using Laplace…

Q: Using Laplace transforms, solve the differential equations (D+ 1) y, + (D- 1) y2 = e- (D+2) y, + (D+…

A:

Q: 3. Solving the following problem using Fourier transformation method. du d²u a² -= 0, (t> 0, -∞0 < x…

A:

Q: Transform: F (s) 18-16 s²-08-13 Of(t) = 4e 3 sin2t – 4e-3t 31 cos2t O f(t) = 4e³t cos2t 4c sin2t O…

A: Given: F(s)=4s-16s2-6s+13 To find the inverse Laplace transform.

Q: Calculate r1(t)·r2(t)] and dt [r1(t) × r2(t)] first by differentiating dt the product directly and…

A:

Q: Using Z-transforms, y(k+1)+y(k) given that y(0) = 2. solve the following difference equation: = 14k

A: Solving the z tranform equation

Q: Given that F[f (t)] =(j /@)(e¯J® – 1), find the Fourier transforms of: (a) x(1) =f(1) + 3 (b) v(1)…

A: Since you have asked a question with multiple subparts so as per guidelines we will solve the first…

Q: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

Q: a) Let T(x), n = 1,2,3, ... are the eigenfunctions of the Sturm-Liouville problem; x³y" + 2x²y' + λy…

A: a) The  solution for the Slurm-Liouville problem is explained below, but the values of a, C, and D…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A:

Q: 2) find the fourier transform x(t) = u(t) x(t) ulzt) x²(t) = u(+ + 5) -

A: xt=utxt=u2txt=ut+5xt=ute-jw0t

Q: D

A:

Q: d d. Calculate [r(t) r2(t)] and dt [r(t) x r2(t)] first by differentiating dt the product directly…

A:

Q: Q.3 (a) If F(a) = F{{(x)} is the Fourier transform of f(z), then show that F{f(ax - b)} = Ja where a…

A:

Q: Use the InverseFourierTransform function of Mathematica or Wolfram Alpha to find the (spatial)…

A: We are given the spatial Fourier transform of a spatio-temporal function u(x,t) as : u(k,t) =…

Q: 2. Use the Fourier transform to solve this transport equation for u = u(x, t), defined on the whole…

A: Given that                       2ut-3ux = 0 and  u (x,0) = e-x2            We can write this as…

Q: 5. 2y"+3y"-3y'– 2 y = e',

A:

Q: Exercise (2): Find the inverse Laplace transform of the following functions. 59}. (1) L- (2) L-1 (3)…

A:

Q: Find invertible representation of Y, = 0.9Y;-1 + e; + 0.5e;-1

A: Given: time series AR(2) process  Yt=0.9Y(t-1) +et+0.5 e(t-1) Then find invertible of Yt?

Q: Find the inverse Laplace transform for (a) F(s) = (s2 – 2s + 5)

A: # We are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: When will the method of Frobenius yield two linearly independent solutions to a second order ODE?

A: Let x=a be a singular point of an second order ODE with variable coefficients. To solve this kind of…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.