1.14 If r(t) = (312-4)i+j+(+3)k, whcre (i. j. k) is a constant standard basis, find i and F. Deduce the time derivative of r xr.

Q: 1- Find the Laplace transform for these functions (a)f(t) = e3t + 8 (b) f(t) = cos(6t) + 7sin(2t)…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: У" +у%3 и, (0) — из- (); у(0) — 0, у'(0) %3D 0.

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Find the kernel of the following differential operator. D3 - 10D2 + 25D = 0

A:

Q: 1. Determine the following Laplace transforms: s+% L*(- `s² – 3s + 9' i) ii) L((1² +e cos 2at…

A: As per our guideline we are supposed to answer first three subparts.kindly repost other question.…

Q: { Vo, æ L,

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Q: Which boundary conditions of the Sturm-Liouville problem y" + iy 0, 0 < x < 1 determine the…

A: Given,         f(x)=∑n=1∞bnsin(πnx)

Q: Compute the Laplace transform of the given function. 1. e6t + 5 + e4t + 5t cos (2t) + 7 sin(3t) 3.…

A: The solution for asked question is given as

Q: Calculate the Laplace transform of the following: f(t)=cos^2(3t) 1 S а. 2s2+72 3s b. 2s²+71 1 с. -…

A: Use the formula: cos2t=cos 2t +12

Q: Use Laplace transform to solve the following initial-value problem. У" - 2у +5у%3D1+t;y(0)3 0;y'…

A: Given The given problem is y"-2y'+5y=1+t y0=0y'0=4 Use Laplace transform formula…

Q: 2) Find the homogeneous linear ODE for which the given functions are Basis. -2x -2x , N, = Xe ", y3…

A:

Q: 7. By using the Fourier transform, find a solution for the following problem (P Ju(1, x) = 4u.z(t,…

A: The complete solutions are given below

Q: - 3t +2 (b) 24 2. (a) 15

A: Topic = Laplace transform

Q: Find Laplace Transform of the following differential equations. 1. 2+52- 3 = 0 given that when x =…

A: Here we have to find out Laplace transform of given differential equation.

Q: 6. Show the validity of the following the 2-D discrete Fourier transform pairs: (а) б(х — Хо, у —…

A: (a) Given,                  δ(x-x0, y-y0)↔e-j2πux0M+vy0N

Q: Solve the following initial-value problem by using Laplace transforms У"-2y'-30е^-3t, У (0)%-1,…

A: Solution of ordinary differential equation with constant coefficients: Suppose we wish to solve the…

Q: 1. Use the Laplace transform to solve the IVP: y" – 4y' = 6e3t – 3e¬t, y(0) = 1, y (0) = –1 %3D

A:

Q: Compute the Laplace transform of the given function. 1. e6t + 5 +e4t + 5t 2. cos (2t) + 7 sin(3t) 3.…

A:

Q: 8. Prove that the differential operator M: C² [a,b] → C[a,b] defined by d²u du Mu= 2+3u dx is a…

A:

Q: Find the eigen value and eigen function of the following homogenous integral equation a(t) = ) st +…

A: The homogeneous Fredholm equation is  fx=λ∫abKx,tftdt.  Here, Kx,t is the kernel. The non-zero value…

Q: у" + 4y' — 12у %3D —15е-3X У(0) %3 3 dan У'(0) — 9

A:

Q: 1 G(s) = (s + 10)(s + 1) - Find the Z-transform of the system

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

Q: 25. Solve the BVP using the Laplace transform method PDE: un = c¯Ux 0<x< ∞, 0st<∞ ВС: и(0, г) — 0…

A:

Q: Choose the inverse Laplace transform of the function 7s +9 s2 – 6s + 13 None of the others O…

A: Given 7s+9s2-6s+13 Suppose fs=7s+9s2-6s+13 Here, we have to find the inverse Laplace transform of fs…

Q: У" + 4y' — 12у 3D —15е-3X У (0) %3D 3 dan у (0) %3D 9

A:

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

A:

Q: 3.17 Use Laplace transforms to find the solution to the follow ing set of equations dt dy2 42 +…

A: Set of equations given as,

Q: (c) Use the Laplace Transform operator to solve the IVP 3y" + 10 y' + 7y = 4 y(0) = 0 y'(0) = 0

A:

Q: Please solve this differential equation question. thanks!

A:

Q: H:3: Expand the following function into its Fourier series : f(t) = cost & te [-π, π]

A:

Q: 4. (a) 4 sin 3t (b) 3 cos 2t

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Q: Find the kernel of the following differential operator. D3 - 10D2 + 25D = 0 Thanks

A:

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

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Q: Use a LaPlace transform to determine the solution of the following systems with differential…

A: The system of differential equations is x' +4x+3y=0y'+3x+4y=2et. Apply Laplace transform: sXs-x0…

Q: b) Use Laplace transform to solve the system of differential equations UTM UTM UTM dz dt - I = 4y,…

A:

Q: 4. Use Laplace Transforms to solve the following initial value problem (IVP): y"(t) + y(t) = f(t),…

A:

Q: 13. Compute the Laplace Transform of f(t) = t°e" +e* sin3t. 4 1 A) (s+ 2)'s² +4s + 13 2 B) (s –…

A:

Q: 1.14 If r(t) = (3r2-4)i+j+(( +3)k, where (i.j.k) is a constant standard basis, find i and F. Deduce…

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

Q: (2) Given that "dw and ewz +e twz = 2 cos(wz), we obtain by applying the inverse Fourier Transform:…

A:

Q: Q3: Find the solution of the Laplace transforms of the following functions: L-1 ¹ [-35 -3s2-12s-87…

A:

Q: 4.Find the Laplace transform of each of the following functions: a.f(t) = t b.f(t) = t2 c.f(t) = tn,…

A:

Q: Show that d() = ñ[6(w − K) + 6(w + K)] is the Fourier transform of cos (Kt).

A: To prove dw=πδw-k+δw+k is the fourier series of cos(kt)

Q: y" + 4y' + 3y = 1– Uz – U4 + Ug , -

A:

Q: 2 1 Given the vector field F=rcosoa,+ -sine ae +rap' After solving for the question, which of the…

A:

Q: y" + ay' + by = 0 for the given basis. 16. e2.6x -4.3x e 18. cos 2Tx, sin 2Tx

A: Ques 18 is asked to be solved.  Given : differential equation y'' + ay' + by = 0, Basis is Cos 2 pi…

Q: What is the formula for the Hermite basis functions?

A:

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: Please solve this Differential Equation question. Thank you!

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Q: 1- Find dwi dt at the given value for w ==+2,x = cos (1), y = sin (1),z = w =-+ at = 3

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Q: Compute the Laplace Transform of the following differential equations (a) 3- dy(t) + 3y(t) = u(t) dt…

A:

Q: 1.Solve the Laplace transform of the following IVP i.y" + 2y' + 2y = 0, ii.y" + 4y' + 13y =…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.