Solve the third-order initial value problem below using the method of Laplace transforms. y'' +2y"-33y' - 90y = - 180, y(0) = 2, y'(0) = 16, y''(0) = 70 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t) = (Type an exact answer in terms of e.)

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: 2. Finish solving each IVP by finding y(t), the inverse transform of Y(s). Do not use convolution…

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Q: 2. (a) Use the method of Laplace transforms to find the solution y(t) of the initial value problem…

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Determine £-'{F}. 2 4s + 59s + 195 F(s) = (s + 6) (s + 3) Click here to view the table of Laplace…

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

A: Converting the equation in Laplace transform:…

Q: X 7.5.23 Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem…

A: Here we use Second Shifting Property and Laplace Transform of Derivative as follows Step (1)Laplace…

Q: (iii) Find Laplace transform of the following using the properties of the transform: te-3t (iv)…

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Q: Determine L '{F}. s?F(s) s+5 + 3sF(s) – 10F(s) = %3D 2 s+ 6s

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Q: 4s +4 (c) Find the inverse Laplace transform of Y(s) — ² + 4s +13) (d) Find the inverse Laplace…

A: The given problem is to find the Inverse Laplace transforms of the given functions Y(s).

Q: (d) * + 6 + 58x = 116, x(0) = 0, (0) = 1

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Q: Q1: using Laplace transforms to find the output x(t) for the following problems, the initial values…

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

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Q: Solve the initial value problem below using the method of Laplace transforms. ty" - 2ty' + 2y = 8,…

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

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y" +y…

A: The solution is given as

Q: (A)Find Laplace transform of the functions : ) S(x)= 4e" sin 3rsin Sx (1) /()-6 sinh 6 (i) (B) What…

A: Laplace Transform  Given a function F(t) defined for all real t≥ 0, the Laplace transform of F(t) is…

Q: Use laplace transformation to solve the following differential euqations. Show all the steps…

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Q: : Find the Laplace transforms of (i) (t – 2)°u(t–2) (ii) e¯"u(t - 2)

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Q: . Sketch the slope field of the ODE y = -xy. Hence sketch its solutions. Hint: Begin by showing the…

A: Given:  Differential equation y'=-xy. To Find: Sketch the slope field and determine the general…

Q: Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the…

A: In part (a) we have to find the Fourier transformation, Given, f(γ,p,t)=e-γtsin pt  t>0,0…

Q: How did they get Y(s)? I tried, but I don't get how to convert the y' notation.

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Q: (D² + 2D- 3)y = sin 2x; y(0) = y'(0) = 0 (Use The Laplace Transform)

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Q: Use Laplace transforms to solve the following initial value problem. x''+x=sin 2t, x(0) = 0, x'(0) =…

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Q: Determine L '{F}. 4s +3 SF(s) – 5F(s) = 2 s+ 10s + 25

A: If f(t) is defined for all positive values of t and if ∫0∞e-st f(t) dt=Fs, then  Lft=∫0∞e-st f(t)…

Q: The following is an IVP: Let's introduce Y(a) = C(v(t)) +4y= cos(2), v(0)=3, (0)-8. Part 1 Apply the…

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Q: Use laplace transformation to solve the following differential euqations. Show all the steps…

A: Some of the properties of Laplace transformation…

Q: Use Laplace transforms to solve the following initial value problem. x"' + 25x = sin 8t, x(0)=0,…

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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: Q6. Solve the following difference equation using z-transforms: Yn+1 + 3yn = 4√n-2, yo = 2

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Q: Perform the following inverse Laplace transforms (5+(2))3. 5-(2) 52+(2)] 2)115+12))? (5+ /2). S+(2).…

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Q: QL using tables of Laplace Transforms and operational theorems, determine (1) L [5 Sin (3t) +8…

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