Use the Laplace transform to solve x(4) + 13x" + 36x: = 0 (3) given initial conditions x(0) = 0, x'(0) = 2, x" (0) = 0, and x (0) = -13

Q: æ' + x = 2+ 8(t – 1), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = help…

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Q: 5. y' = (x + y)²

A: Given: y'=(x+y)2

Q: Solve the given initial-value problem using the Laplace transform: -{- = x(0) = 5. x' + 3x if 0<t<4…

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Q: If f(t) = e-t3 – 2 sin 2t determine L{f" (t)} %3D

A: Formula Used: L{eattn}=n!(s-a)n+1L{sin at}=as2+a2L{f''(t)}=s2L{f(t)}-sf(0)-f'(0)

Q: - y"+10y'+25y=0y(0)=0_y"(0) = 10

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Suppose that f has an inverse, ƒ(2) = 5, and f'(2) = What is (f~')'(5)? %3D

A: (a) Given that f has an inverse, f(2)=5, and f'(2)=-34 As  f(2)=5 so, f-1(5)=2

Q: Show that d(w) - = [6(w− 1) + 6(w+1)] is the Fourier transform of cos(t). Show that d(w) = −ix[8(w −…

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

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Q: a' +x = 6+ 8(t – 4), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} = help…

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Q: Use Laplace transforms to solve the following initial value problem. x'' - 9x = 5t; x(0)=x'(0)=0…

A: The given initial value problem is x''-9x=5t, x(0)=x'(0)=0 The laplace differential formula is…

Q: Q3. (a) Consider the continuous function f(t)=sin(2xnt). i) What is the period of fſt)? ii) What is…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: 2- Solve the fractal differential equation Day + y = 5e²x With a = a = and and y(0) = 1, Using…

A: Given Fractal Differential Equation:  Where ​ and .Objective: To solve the given fractal…

Q: F{6f"(x) – 2f' (x) + 7f(x)} =

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Q: Use differentiation in time domain to solve the the Laplace transform: y"+7y'+12y=21e³t; y(0)=7/2,…

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Q: In each of Problem, write the Fourier integral representation (14.1) of the function and determine…

A: The Fourier integral representation of a function f(x) is given by:   f(x) = (1/√(2π)) ∫[from -∞ to…

Q: Use the laplace transform to solve 3r'-y=21;x'+y'-y=0; x(0)=y(0)=0

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Q: 7. Use the Laplace transform to solve the difference equation 3x (t) 4x(t-1) = 1, x(t)=0 for t < 0.…

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Q: Use Laplace Transforms to solve the initial value problem. x"+x = sin2t; x(0)=0=x'(0)

A: Solution of Intial value problem using Laplace transferom

Q: Calculate two iterations of Newton's Method for the function using the given initial guess. (Round…

A: In this question, we will find the solution by using the Newton method.

Q: What is the Fourier transform of 8(x) dx F(k) = 100 = 2T -ikx 8(x) =?

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

Q: Use (8), • S* f(1) dt = £^¹{F(5)}, to evaluate the given inverse transform. (Write your answer as a…

A: we know that laplace transform of e^(at) is (1/(s-a)).

Q: Suppose solving an equation by Laplace transform results in 4 (s+ 18) Y (s) : %3D (s+9)² * Evaluate…

A: Laplace transform of the function y(t) is defined as Y(s)=∫0∞e-sty(t)dt, where s&gt;0. Since the…

Q: x' + æ = 9+ 5(t – 2), x(0) = 0. Find the Laplace transform of the solution. X(s) = L {x(t)} help…

A: Given that, x'+x=9+δ(t-2),x(0)=0 To find the laplace transform for the given equation, Take,…

Q: Use Laplace Transform to solve the given Initial Value Problem.  y''+9y=cos(3t)  y(0)=2 y'(0)=5

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Q: Use the Laplace transform to solve the following initial value problem: y''+8y'=0, y(0)=-2,…

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Q: Using the Laplace transform solve the following initial value problem x" - 2x + x = t - sint, x = x…

A: The given initial value problem x''-2x'+x=t-sin t, x=xt, x'0=x0=0. We have to solve the initial…