(CONTROL SYSTEM) 1: Direction: solve for y(t) if all initial conditions are zero. Use Laplace transforms a) dy3 dt 3 + ²-15-12y = 5u(t). dt

Q: 5 5 ロジー 12y+y="/sin(x) (0) = 0,(0) 2

A: We have given DE,Taking Laplace transformation on both sidessubstitute the given initial conditions…

Q: Y = f+₁ + fot-, h= 71

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Q: Find the general transformation of the second order, constant number, non-homogeneous linear…

A: In order to find the solution of the given question, we will use the following concepts: 1. The…

Q: Solve by Laplace transforms. (Do not use Heaviside coverup.) Y – 2 y(7)dr = 2t?. -

A: Given that y-2∫0tyτdτ=2t2. Solve this using the laplace transform.

Q: Use Laplace transformation to solve the initial value problem y' + 2y = u(t) sin (2t), y(0) = w,…

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

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Q: Solve the ODE: xy"+2y'-xy Oby using the Frobenius method.

A: Given that ODE: xy''+2y'-xy=0                    .....1 We know that the solution to this ODE is:…

Q: 25. Find the general solution of the equation dy = 2y + 2e-. dt (This equation is linear, but please…

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Q: * + 5x + 6x = 5sin (2t)

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Q: Q: Solve the following set of simultaneous equations using Laplace Transfor d²y 4² - x = y; + dt²…

A: This is the question of Laplace Transform.

Q: d2y/dt2+a2y=b sin wt  ( laplace transform )

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Q: Use the Laplace transformation to solve the following ODE: y''-y'-12y=2e2t, with y(0)=7, y'(0)=0.…

A: Given: The given ordinary differential equation is y''-y'-12y=2e2t with y(0)=7 ,y'0=0

Q: Nap Lajoie has a lifetime batting average of 0.338. Assume that Nap Lajoie came to bat officially…

A: Given : Nap Lajoie has a lifetime batting average of 0.338 and came to bat officially six times…

Q: Q1: Solve using Laplace transform y + 4y = 8(t), y(0) = y (0) = 0

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Q: (4) Let f(x, y) = e-y. Find the linearization of f at an appropriate point and use it to…

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Q: 4.0 f(t) = 3 – e-3t + 5 sin 2t

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Q: Use Laplace transforms to find the general solution for y(x) :   d2y/dx2 + 2 dy/dx + 2y = 3e-x

A: Step 1: SolutionGiven differential equation: dx2d2y​+2dxdy​+2y=3e−xUse Laplace transforms to find…

Q: Determine the constants a, p, yo and y'o so that 3S +3 Y(s) = (s + 2)² is the Laplace transform of…

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Q: + = -2 a) Find homogeneous solution vectors and show that they are linearly independent. b) y1(0)=-1…

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Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

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Q: Solve for P(t) using the given information. d² p dt² = (6t, 2+3t), P(1)=(2,1), P'(1)=(3,2)

A: We have to solve given Questions.

Q: the form of the transforms found for the functions above, state what form (c) Find the roots of the…

A: Here, we are given the following differential equation.         16d2ydt2+8dydt+145y=0, y=2, dydt=0…

Q: Find: x - 4x + 13x = 2 sint, x (0) = 1, x(0) = 0 (a) Obtain the solution to the ODE by solving for…

A: Solution of the differential equations using Lapalce transfermation and homogeneous method

Q: 4.1 Solve by Laplace Transformation U+ + Ux₁ = xt with I.C: u(x₂0) = Sinx ; u(ost) = 0

A: 4. To solve the given partial differential equation (PDE) using Laplace transform, we will follow…

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…