Q1.Solve the following IVP by mean of the Laplace transform P.D.E. u = a²uxx -∞0 < x < ∞0,0 < t <∞ I.C. u(x,0) = sinx, -∞ < x <∞

Q: Find the inverse Laplace transform L-1{F(s)} of the given function. 4 F(s) = s2 + 4 Your answer…

A: Given,           Fs=4s2+4

Q: 5s + 20 F(s) = s2 + 8s + 97

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Q: ind the Laplace transform of the periodic function f(t) = 50=[²₁ 1 for 0<t<2 for 2<t<4

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Q: Q4 Solve step Functions in Laplace transform t < 6 x ≥ 0 f(t)= = { = 8+ (-8+ (t-6)²

A: The given problem is to find the Laplace transform of the given unit step function. Use the…

Q: 6. f (x) = 3sin2xcos2x 7.L [2x5 + 3x3 - 10x? – 4] 7 8. L [3x2]

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Q: From a Laplace Transform form, we have the following expressions: s - w I) L{ewt cos(ßt)} (s – w)2 +…

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Q: Find the inverse Laplace transform of the function as + b H(s) = (s – a)2 + 32 °

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Q: Which of the following is a parameterization of the line that passes through the point (-1, -2) with…

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Q: Find the cosine transform fe(w) of f(x) for f (x) = -6 if 0 2. f.(w) %3D

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Q: 6. Use the Laplace transform to solve the following IVP. The table is on the next page. y" + 3y -…

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Q: Use convolution and Laplace transform to evaluate y''+y=sin(t) , y(0)=1 , y'(0)=-1

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Q: 2a. Determine the solution of the following problem using the concept of derivative and integral…

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Q: If (p) is the Fourier Sine transform of f(x) for p>0, then prove tha Af(x}} = - (- p) for p<0.

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Q: 3. Use the definition of Laplace transform to find L{t²H(t-5)}.

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Q: 8. Express the given function using unit step functions and compute its Laplace transform y sin t N…

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Q: f(t) = when 0 k

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Q: 4. (20 points) Use the Laplace Transform to solve the IVP y' +2y 2e", y(0) = 3

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Q: 4. Using the definition, not the table, find the Laplace transform of (a) f(t) = −3 (b) g(t) = 4t…

A: Laplace transform of the function

Q: Which of the following is a true statement? d (10) = 5 (104) da O The equation of the tangent line…

A: (1) ddx(105) = 0         ∵ddx(c) = 0  statement is False(2) The equation of the tangent line to the…

Q: 6. Use the Laplace transform to solve the following IVP. The table is on the next page. y" + 3y' -…

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Q: . Use the Laplace Transform Table (LTT) to find F(s) = L{f(t)}(s) if f(t)=t¹+t²e + sin²t - e" sin…

A: Consider the function ft=t4+t2e-t+sin2t-e3tsin3 t. To determine Laplace transform of ft. Laplace…

Q: 2. Use the Laplace transform table to find F(s) for the given function. 1. f(t) = 2t²e-t cosh t.

A: Given - f(t)=2t2e-tcosh t. We know to find F(s) for the given function using Laplace transform.

Q: Write down the qualitative form of the inverse Laplace transform of the followir functions. For each…

A: The given equation of  Laplace transformation is: Poles are the zeros of the denominator the…

Q: 2. Use the Laplace Transform to solve roupa fainalid OSOESTAM y"+y=f(t) subject to y(0)=0=y(0) where…

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Q: Q9. Use Laplace transform to solve the ODE. X-4x +3x =-8cos4t, x(0) =0, x(0) = 0 %3D

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Q: Question. By using Laplace transform, solve the IVP where y" - 3y = f(x); y(0) = 1, y(0) = 0 { f(x)…

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Q: Find the Fourier transform of the following functions: (₁) f(t)= (11) "-(1+t), -12 t ≤0 t-1 04+ ²1 อ…

A: We have to find the Fourier transform of the given functions: (i) ft=-1+t-1&lt;t≤0t-10&lt;t≤10t&gt;1…

Q: Q7. Find the Laplace transform of the periodic function f(t)= sin at for 0<t<¹ 0 for T @ -<t< @ 2π @

A: Sol:-

Q: Find Fourier transform of f (x) = x e¯*, 0 <x <∞.

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Q: Find the inverse Laplace transform L-'{F(s)} of the given function. 10s? – 24s + 96 - F(s) = s(s2 +…

A: To solve given problem first we  do partial decomposition of given function then taking inverse…

Q: 1 1.4 f(t) = || (t– 3) - dt sec 21 cosec 21

A: We have to find laplace transform of the function f(t). First we will solve for f(t) and will find…