2. Laplace Transform of an Integral and a Derivative (a) Consider the function, f(t) = So exp(-37) cos(27)dr. Without integrating, determine the Laplace transform of f(t). (b) Consider the funtion, f(t) = t(d/dt)[exp(-t) cos(t)]. Without carrying out the differ- entiation, determine the Laplace transform of f(t).

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

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Q: 7. Obtain the Fourier sine transform of the following functions: sin wx (c) x² +1' w > 0

A: The given problem is to find the Fourier sine transform of the given function, we have a general…

Q: Find the Laplace transform F(s) of the function f(t) = e"6(t - 3) F(s) = e^(20)

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Q: Find the Laplace transform F(s)=L{f(t)} of the function f(t)=e^(−3t) cosh⁡(5t).

A: Laplace transform of the function, f(t)=cosh(at) is

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

A:

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: Given the function f(t)=e^{2t}sin(3t), find the Laplace Transform, F(s).

A: The Laplace Transform is a tool used to transform a function of a real variable t (usually time)…

Q: Prove that the Laplace Transform of sin(at)+at cos (at) is 2as? (s` +a°)* Please show your Solution…

A:

Q: Solve equation using Laplace transform ÿ +9y = 6 (t -) sin(t), y(0) = 0, y(0) = 0 %3D

A: Given the given equation is y"+9y=δt-π6sint,     y0=0,  y'0=0 Use the property of delta function.…

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

A:

Q: b) Find O Using the chain rule to find de x-1 dy of y= dy of y sin 1-xy ) Using the implicit…

A:

Q: Part A how that L(tnf(t)) = (−1)n ((dnF(s))/(dsn)), where F(s) is the laplace transform of y(t). In…

A: Hi, It is multiple sub-parts, I am going to solve the first part only.

Q: Find the convolution (f * g), after integrating find the Laplace transform of (f * g): f(t) = cos2t,…

A: We have to find convolution (f*g) and the Laplace transform of (f*g) wheref(t)= cos2t, g(t)= et .

Q: {; .0 2 FİND THE LAPLACE TRANSFORM OF THE FUNCTİON WİTH THE HELP OF THE DEFİNİTİON .(DEFİNİTİON…

A:

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: Find the Laplace transform of sin 21, 0<t < 2n S(): 0, 12 2n

A: we have given the function f(t) = sin2t,  0≤t≤2π   0,          t≥2π we have to find the Laplace…

Q: the laplace transform of (t)= t^1/2 as F(s)=sqrt of pi/s, find Laplace transform of 7t^3/2.

A: L7t32=7Lt32Use Laplace Transform table:   Ltn-1/2=2n-1!!π2nsn+1/2=7·3π4s52=21π4s52

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: Part A) How that L(tnf(t)) = (−1)n ((dnF(s))/(dsn)), where F(s) is the laplace transform of y(t). In…

A: The problem is related with Laplace transform.  First in part (A), we have to show that Ltnyt =…

Q: where k > 0. s(s-k)'

A: Using Laplace transform of integrals  L∫0tftdt=1sFs Also,  πss-k=πsFs where Fs=1s-k

Q: use Laplace transform to solve IVP a) y'-3y = 4, y(0) = 0

A:

Q: { , 0 2 FİND THE LAPLACE TRANSFORM OF THE FUNCTİON WİTH THE HELP OF THE DEFİNİTİON .(DEFİNİTİON…

A: We will use the definition of laplace transform