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

Q: 10. Solve the following IVP using Fourier Transform: -00 0, u(x,0) = e, -0 <r < oo.

A: Given ut=uxx, -∞&lt;x&lt;∞, t&gt;0u(x,0)=e-x2, -∞&lt;x&lt;∞

Q: Suppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(7).

A: We have to solve given problem:

Q: 4. Solve the following equation by transforming the Method Laplace (Transform) transform. u(x)= x -…

A:

Q: 3. Use the Laplace transform method to solve the initial value problem r = 6x1 + 11r2, r = -4x1 –…

A:

Q: у" (() + у(t) 3 0 y(0) = 0 y'(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: ce transform to solve the given in = 0, y'(0) = 1, y" (0)

A:

Q: 2w Inverse fourier transform of is w²+9 Select one:

A:

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: Find the Fourier transform of ƒ (t) = 2 for -T≤t≤0 2 for 0 ≤ t ≤T

A: We have to solve given problems:

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: 55. By the transform method, solve Ut = Urx + g (x,t), u (x, 0) = f (x), 0 0, 0 0.

A:

Q: Use laplace transform to solve the initial value problem; a) y''+9y=cos3t,y(0)=2, y'(0)=5.

A: We shall use Laplace and inverse Laplace transform to solve this

Q: 2 The inverse Laplace transform by using integral of transform s(s2 +2s+4)

A:

Q: 2s3+ 4s²+1 F(s) = (s²+ 2s+17)(s²+ 4s+20)

A:

Q: 10. Solve the following IVP using Fourier Transform: -00 0, u(x, 0) = e¯**, -00 <x < o0. %3D

A: Given: Let us consider the given, ut=uxx,              -∞&lt;x&lt;∞,   t&gt;0ux,0=e-x2,…

Q: 4. Determine the Fourier transform of the given function: 1 (t) = {2t - t, 2t - 1, 0 < t < 1 0<t<2…

A:

Q: 2s²+7 F(s) (s+1)(s+2)(s²+ 2s+5)

A:

Q: 4. Find the inverse z-transform of X(Z) = (22-4) (2+3) Xx and also find o, 1,

A:

Q: 10) Use the Laplace transform to solve the given initial-value problem. y'-y = 2 cos (3t) when y(0)…

A:

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

A:

Q: Q2) Solve the initiai value problem by Laplace transform. y" +4y=cos 2t y(0) = 1 , y'(0) = 1

A:

Q: Q11) Determine if 8 (t) and 8' (t) even or odd by utilizing properties of Fourier transforms. What…

A: Given: δ(t) and δ'(t) are real functions. Fourier Transform property : Fourier Transform of even and…

Q: 3. Use a Fourier transform to solve the equation d'y - y? = 0 dx2 with initial conditions y(0) = yo…

A: Given: d2ydx2-y2=0 To find: Solve the equation by using Fourier transform.

Q: Use the Fourier sine transform to solve the following BVP with 0 0 10₂4+02=0, მყ2 u(0, y) = 0, u(π,…

A:

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

A:

Q: 22) Solve the initiai value problem by Laplace transform. y"+4y cos 2t y(0) =1, y'(0) = 1

A: In this question, we are asked to solve the Initial value problem by Laplace transform Equation :…

Q: 2) Sólvé thẻ điffèréncé équation using z-transform yk+2 - 3 Yk+1 + 2 Yk 0, with yo = 0, y, = 1.…

A:

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

A: We need to use Laplace transform to solve this differential equation.

Q: (7) Solve the PDE by Laplace Transform a²w aw <=100 +100 + 25w, ar² at w(x, 0) = 0 if x ≥ 0, we(x,…

A: The given P.D.E is                       ∂2w∂x2=100∂2w∂t2+100∂w∂t+25w,wx, 0=0 if x≥0, wtx, 0=0 if…

Q: Obtain inverse Laplace transform 1. (s+2)

A: Given expression is e-4s+23.

Q: 3. Use a Fourier transform to solve the equation d²y dx2 y 0 with initial conditions y(0) = yo and y…

A: Given: d2ydx2-y2=0 To find: Solving the equation by using Fourier transform.

Q: Б) у —у +Зу — 5у%3D—-бе-t У () %3 1, у (0) %3D2, у' (0) %3D— 4

A:

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

A:

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

A:

Q: 6. use Lapiace Transform to solve the lmitial valwe problem: y" +y = hlt) , ylo) = 2, y'lo) =0 where…

A:

Q: 5. Use Laplace transform technique to solve v"-y'-6y = 0, Given v(0) = 1 and y'(0) = -1

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

Q: 5. Use Laplace transform technique to solve, y" 3y' 2y 0, given y(0) I and y'(0) 0

A:

Q: 7) Use the Laplace transform method to solve the Volterra integral equation: u (x ) = 1-x - (x –t )u…

A:

Q: x(t)=1(t+4T)

A:

Q: 9. Solve the IVP using Laplace transform: x' – x = 2cos5t, with x (0) = = 0.

A: Given equn isx'-x=2 cos 5t with x0=0taking both the side laplace transformation we get…

Q: 5. Use the Laplace Transform solve the IVP: x' + y = t (4x + y' = 0 x(0) = 1, y(0) = 2

A: Theory : The Laplace transform of a second order linear differential equation : y" +α y' +βy =f(t)…

Q: 2) Solve the difference equation using z-transform yk+2 - 3 yk+1 + 2 yk = 0, with yo = 0, y, = 1.…

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

Q: 4. Use Laplace transform technique to solve , y"+2y'+2y = e given y(0) = -2 and y'(0) =-1 %3D

A:

Q: Find the inverse Laplace transform 01 2 Ou44(1-4) usinh(t — 4) O sinh4(1-4) 0 1 u4cosh4(1-4) 01 4…

A: Given problem:- Find L-1e-4ss2-16

Q: O Show that the Fourier transform of | 3 -2<1<2 0 otherwise f() = {0 6 sin 20 is given by F (@) =

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

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

A: We have to find general solution of given differential equation using Laplace transform Method.