y' = 8x x(0) = 1 %3D x' = 2y y(0) = 0 %3D

Q: Find the inverse Laplace transform of the following function by using Theorems and tables 2s + 5 +…

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Q: Find the laplace transform for the expression : e (f +3t + sin(5t))

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Q: find the laplace transform of the equation: f(t)= 2t^3 e^-4t

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Q: Apply the properties of laplace transform including the linearity property, shifting property, and…

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Q: f (t)%3 3e ' cosh ( In 2r)

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Q: Find the Laplace transforms of the functions. f(t) = 3t^5/2 - 4t^3

A: Laplace transferom of the function

Q: Find the Laplace Transform for the function e-Nt sin²(Nt)

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Q: find the inverse Laplace transform of the given function of 4e^(-2t) / (s(s+4))   Thank you for…

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Q: Solve equation using Laplace transform ÿ + 9y = 8 (t -) |sin(t), y(0) = 0, ý(0) = 0

A: Formulae:  1. Lf(t)δ(t-a)=e-asf(a) 2. Lf''(t)=s2F(s) - sf(0)-f'(0) 3. L-1e-asF(s)=H(t-a)f(t-a),…

Q: 2. Find the inverse transform of 2s² +5s-6 $³3s2-13s +15

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Q: Q3\Find the Laplace transform of: a) t et * sin(4 t)

A: Given  f(t)= tet sin4t

Q: 2. Verify the following property of the Fourier transform: F(u(x + a)) = e-ial a(z)

A: Given::- Verify the following property of the Fourier transform: F(u(x + a)) =e^ -ia xi hat u( xi).

Q: Find the Fourier transform of 6e-lt

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Q: 3 s + 10 s – 40 (t) (s³ – 4 s² – 7 s + 10) (s – 4) s

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Q: Determine all values of k for which the following set of vectors spans R4. You can select 'always',…

A: We have to find the value of k for which given vectors will span R4. 3-102,0-101,1013,002k

Q: Q3\ Find the Laplace Transform to the following function L sin2t cos3t

A: Using Laplace transform

Q: 1. Find the equation of a line perpendicular to y = 1 through A(-1, 1).

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Q: Find the inverse laplace transform of H(s)= 8/(3(s^2) + 12) + 7/s^5

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Q: Determine the Laplace transform of L(sinh 5t * cos t)

A: Explanation of the answer is as follows

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: 4. Find the Inverse Fourier transform of Te-l@l.

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Q: Since (7t^2) *e^(mt) - (7t^2) *sinh(at) = (t^2)(7e^(mt) - 7sinh(at)) What should you take the second…

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Q: Find the Laplace transforms of the functions. f(t) = Cos^2(2t)

A: Let ft=cos22tTo find: Laplace transform of the function ft.

Q: A coat has an original price of $48.99.  Gloria wants to calculate the final cost of the coat…

A: See the solution below.

Q: Summarize the method used for solving linear, first-order ODE's. What theorem is used to justify…

A: A first-order linear differential equation is written like dydx+Pxy=Qx             (i) Here, Px, Qx…

Q: Use the solution method from this example to find a basis for the given subspace. {[³] [_;)} { S =…

A: We have the space S spanned by two vectors [2,5] , [6,-1].We will show that these two vectors are…