Write down the solution to x" - 2x = e, x(0) = 0, x'(0) = 0, as a definite integral. Hint: Do not try to compute the Laplace transform of f(t) = e¯ = e-t².

Q: find the root of the equation  f(x)= -x/2 + sinx =0 using bisection method in the interval [1,3]…

A: given function fx=-x2+sinx=0 find the root of the equation using bisection method in the interval…

Q: Consider the following ODE y' = y+t/y+1 Which kind of ODE is ?

A: Given ODE is y'=y+ty+1. Simplify y'=y+ty+1. ⇒dydt=y+ty+1⇒y+1dydt=y+t⇒y+1dydt−y=t..........1 Since,…

Q: 7. Evaluate y" + y' = t; y(0) = 1 , y'(0) = -2

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

A: Given: The difference equation, 3xt-4xt-1=1, xt=0 for t&lt;0   To solve: The given difference…

Q: f(t) = {, - 2 2 -2

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Q: Solve using Laplace transform y"-2y' +5y=1+t, y(0)=0, y'(0)=4

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Q: 2) t? t et sin 4

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Q: Use the laplace transform to solve 3x'-y=2r;x'+y'-y=0; x(0)=y(0)=0

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Q: Use Laplace transform to solve the DE. d²y_3dy = 9 dx² dx where x=0, x=0 and dy=0 dx

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Q: Use differentiation in time domain to solve the the Laplace transform: y"-y'-6y=0; y(0)=6, y'(0)=13

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Q: Find the differential operator which will annihilate the function 2x + r³ – sin 2r.

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Q: 3. State and explain the Convolution Theorem for Laplace transform

A: We have to state and proof  the convolution theorem of laplace transform.

Q: If g(x)= J JAtes dt, find g'(2) 4+t5

A: If H(x)=∫bxh(t)dt and the function h is continuous in the interval: b, x, then using the fundamental…

Q: Let F(x) | sin (4t?) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.8 Use this polynomial…

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Q: 2x" - 3x' + x = 0 x(0) = 2, x'(0) = −1

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Q: S(1) = >1

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

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Q: ) 3x - 4x= sin社 ; at t=0,x==

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Q: 1. Find the forier tansform of f(t) = 8(t) + 2e-3lt| %3D

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

Q: Write down the definition of the laplace transform in terms of an improper integral and use it to…

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Q: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

A: Find the laplace transform of f(t) =1/4 e^2t sin(2t)

Q: let g’(t) represent the rate of growth of a dog, in pounds per year. What then, does g(t) represent?…

A: Given: g'(t) represents the rate of growth of a dog in pounds per year.

Q: Use the Laplace transform to solve y' - v = te'sint, y(0) = 0

A: To solve the given IVP, first we take the Laplace transform of differential equation and then we use…

Q: kx _f(x) = ek

A: The Fourier integral of a function f(x) is defined as:F(ω)=∫−∞∞f(x)e−iωxdxTo find the Fourier…