Find aT in the decomposition of a(t) into tangential and normal components -3t ) and t=-1.

Q: .) Use method of Laplace Transforms. y"-6y +13y=0, y(0) = 1, y (0) = -3.

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Q: Find the Laplace transform of the following: 1. y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0) = -2

A: To find the Laplace transform of the problem.

Q: Use the Fourier transform to solve the BVP Urr + Uyy = 0, -0 0 u (x, 0) = f (x) lim u (æ, y) = 0,…

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Q: Use the Laplace transform to solve the given initial-value problem. 2y" + 3y" — Зу' - 2у %3D е",…

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Q: Find the general solution of the DE s

A: Given: - The differential equation is, dydx=2yx+x3y+xtanyx2 To find: - The general solution of the…

Q: Solve the IVP using Laplace transforms. x(0) = 4 15. x'(t) = t², %3D %3D

A: Here we will use Laplace transform method to solve the differential equation.

Q: Solve the IVP using the Laplace transform. y" – 7y' + 10y = e'", y(0) = 2, y (0) = 0

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Q: Use Laplace transforms to find the solutions to the following first order differential equations.…

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Q: e Transform of the functions 1. e2t (

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Q: Find the Laplace transform of the equation: y′′+y′−3y=e-2t when y(0)=0, y′(0)=0

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Q: Find the solution of the differentical equation using Laplace transform +64 dt given that %3D 남 (o)-…

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Q: Find x(t) and Y(t) using Laplace transform.

A: The given pair of equations dxdt=2x-3ydydt=y-2xx0=8, y0=3

Q: PROBLEM B dx ·+ 9x = 12 WHERE : x(0) = 1 dt

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Q: Find the Laplace transform of 1. f(t) = [1 − u₂n(t)](2 sin t - sin 2t) - 2

A: Properties of the Laplace transform Laf(t)+bg(t)=aF(s)+bG(s)Lsinat=as2+a2Luc(t)sinat=e-css2+a2

Q: Find the Laplace Transform of h(t) =t² sin(2t) 4s2 –3 A H (s) (s²– 4) 3 3s2 – 4 (B) H (s) = (s²+4) 2…

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Q: Find the Laplace transform, Y(s), of the solution of the IVP y" + 3y + 2y = cos(2t), y(0) = 0, y'(0)…

A: The given initial value problem is y''+3y'+2y=cos(2t), y(0)=0, y'(0)=1. Find the Laplace transform…

Q: find the decomposition of a(t) into tangential and normal components at the point indicated = (4 –…

A: To find the decomposition of a(t)

Q: Use the Laplace Transform operator to find the Solution of the IVP, 3y + 5y- 2y = 4x°. y(0) = 0 У…

A: Given 3y''+5y'-2y=4x3  y(0)=0  y'(0)=0Taking Laplace Transform on both sideL(3y''+5y'-2y)=L(4x3)…

Q: Find the Z transform of [cos (ax), x20 f(x)=: 0, x<0

A: Given, fx=cosax,x≥00,x&lt;0 As we know that, Ze-ax=1+e-aτ+e-2τz-2+...=11-e-aτz-1=zz-e-aτ

Q: Use method of Laplace Transforms. y"-6y +13y = 0, y(0) = 1, y (0) = -3.

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Q: Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: Determine the Fourier transform of f(t) = te-2t u(t), where

A: Given ft = te-2tut where ut =0     t&lt;01    t&gt;0 The Fourier transformation is given by Fw…

Q: f(t) = [1– u2m(t)](2 sin t – sin 2t) U2n

A: Some of the properties of Laplace transformation Lsinat=as2+a2Luc(t)=e-cssLuc(t)g(t)=e-csL[g(t+c)]

Q: Find the Laplace transform of 0st<1 f(t) = {2 - t, 1st<2 2 <t

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

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Q: d2y/dt2-y=t2 (laplace transforms)

A: To solve the given differential equation using Laplace transform. Here we will use the following…

Q: Solve the Laplace Transform of the equation f(t)= te²ᵗsint

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Q: Find the Laplace Transform of h(t) = t? sin(2t) = ='s 3s2-4 A H(s) = (s2+4) 2 482 – 3 B H(s) =…

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Q: Find the Fourier transform for x[t] = at*u[t], |a| &lt; 1

A: Given function is,

Q: 1- t2 is The differential of u=In, 1+ t2 -2t dt t4–1 (A du = 2t dt t4 - 1 B du = dt t4 – 1 du = -2…

A: to find the differential.

Q: Find the laplace transform of t sin (t) A. 2s/(s2+1)2 B. 1/s2(s2+1) C. 1/s2 + 1/s2+1 D. -…

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Q: Find the Fourier transform of f(t) = {, t 0 12e-t O 2/(1+jw) O 1/(1+jw) O -1(1+jw) O -2/(1+jw)

A: We have to find the Fourier transform.

Q: Exercise 3: Find the Laplace transform of f(t) = cos (t -).

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Q: Show that x(t) * u(t) x(t)dt %3D and find its Fourier transform.

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Q: Prove f(x,y)=ln(x2+y2)1÷2  by laplace equation

A: Given: The function, fx,y=lnx2+y2 and the Laplace equation, ∂2f∂x2+∂2f∂y2=0.

Q: I t los 2t e-を

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Q: Find the Fourier Transform of Sa? – x², for |æ| a f(x) = and hence deduce that (sin s- s coss -) ds…

A: Fourier transform of gx=1 for x&lt;a0 for x&gt;a is ∫-aa1.e-isxdx. Calculate it:…

Q: Find the Laplace Transform of e-t sin2t 2 2s 2 A. ²/+ B. S (s+1)²+4 (S-1)²+4 C. S+1 s(S²+4) D. None…

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Q: Let V = R2 and let 2, Find the Fourier coefficients of (3, 4) relative to ß.

A: It is given that,

Q: use the laplace transform to solve y'' + 9y = cos3t, y(0) = 4,  y'(0) = 2

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Q: Find the Fourier integral representation of t 1 0, f(t) = t, 0,

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Q: Find the Fourier trensfor - at e t 7° F(t) = tくo

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Q: t2, 0 2

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Q: Given x(t) = 5te-3 u(t), what is the Fourier transform of x(t)?

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: 3. Verify that the function u =1/ /x² +y° +: Laplace equation u +u, +u =0 is a solution of the…

A: The given function is u=1x2+y2+z2. The three-dimensional Laplace equation is uxx+uyy+uzz=0.

Q: Obtain the Laplace Transform of 1. L{t³ – t² + 4t} 2. L{3e4t – e-2t}

A: 1.   6s4-2s3+4s2 2.  3s-4-1s+2

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

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Q: Find the Laplace transform of t², -8+ 3t, g(t) = - (t-6)² + 2 cos (1-²), 6 0 2

A: Let us find the laplace transform of the given function g(t) as follows: