The solve of following by using Laplace transforms y"-5y +6y =2u (t-10) ,y (0)= y(0) =0 ,is a) (e-(t-10) – e-2(t-10))u(t – 10) b) (- e2C-10) + Ze(-10)u(t – 10) c) - e?(-10) + e(-10)u(t – 10)

Q: (12) If y = a X"-b X*+1+5 is a polynomial and a » bER , then may by represent dX" by one of the…

A: n order derivative

Q: 2. Start: y= x What transformations occurred? End: y =-9(x-8)² + 5

A: First   shift the graph right by 8 units.  Then  strecth by (-9) units.  Then  shift upward by 5…

Q: Write down Fourier Transform for the following non periodic function.

A: In this question, we have to write the Fourier transform of the non-periodic function. The function…

Q: 7. Using Lyapunov functions, show that the origin is unstable for the ODE i = -x3 ÿ = -y3

A: The solution is given below

Q: 29. 29. Find inverse Laplace transform of 1 (a) g2 — 38 + 2 )b( - 1 s3(s+1)

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Q: 6. Find the inverse Laplace transform of the function (3²-²)(as + b) I(s) = (s² + a²) (s² + 3²)

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Q: Find the Fourier transform of the given function. (a) f(x) = A(2x + 1). A(2x − 1)

A: As per the question we are given the function f(x) as : f(x) = Λ(2x+1) • Λ(2x-1) And we have to find…

Q: L-1 (s-4) (s2-8s-9). A) Find B) Find the Laplace transform of (te-2tcost) (s-1) C) Find L-1…

A: Explanation of the answer is as follows

Q: sinh ot + cos ot

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Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: Use a formula to express y as a function of t if y = 6x + 4x and x = t- 1.

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Q: 2) There is a function F (s) with "different true root state". Make the inverse laplace transform of…

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Q: (a) A(s) = 5s-44 (s-6)²(s+1) -3s

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Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

Q: Compute the Fourier transform of the following function: f(x) = e-a(r-x0)²+iqx (5) where a > 0 and q…

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Q: Find the inverse Laplace transform of 7s + 3 82 + 17 8 >0

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Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

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Q: Find the function f(x) that has Fourier transform (k) = (1+k4)-1.

A: Here we have to find out  .Now from definition of inverse fourier transform , to evaluate this…

Q: Q11) Determine if 8 (t) and 8' (t) even or odd by utilizing properties of Fourier transforms. What…

A: Given: δ(t) and δ'(t) are real functions. Fourier Transform property : Fourier Transform of even and…

Q: State the definitions of direct and inverse Fourier transforms. Then, compute the Fourier transforms…

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Q: f(t) = cos 5t – 3t² s4-6s2-30 s4-6s2-150 а. F(s) с. F(s) s5+25s3 5s3-6s²–150 s5+5s3 5s3-6s2-30 b.…

A: We need to find the Laplace transform of ft=cos 5t-3t2 That is we need to find Lcos 5t-3t2 Now,…

Q: erfind the first agd decond derivatives oh the funchan

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Q: 15. (a) (i) Find the Z-transforms of cos and 'n(n+1) no A (ii) Using convolution theorem, evaluation…

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Q: Which transformation includes a reflection of f(x) = (x – 1)² + 1 over the x-axis? Of'(x) = (-2x –…

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Q: Find the Laplace transform of 1.- L(2x + 3x³ - 5x² + 7x - 1) Value of 3.33%

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Q: 4- (a) Show that XYX = -Y and (b) show that [XY,YZ] = -2iY.

A: a) To show that XYX = -Y, we can use the definition of the commutator [X,Y] = XY - YX and the…