Consider the so called Riccati ODE and let y₁ be a solution. y' = p(t)y² + q(t)y + g(t). Show that: a. The transform 1 y = y₁ + 2 turns the ODE into a first order linear ODE with respect to z. b. The transform y = y₁ + z turns the ODE into a Bernoulli ODE with respect to z.

Q: Find the Laplace Transform of f () =2 sin a +3 cos 2z.

A: This is question of laplace transform . Solution is given below

Q: F(s) f(t); t= 0 A.0 B.9| s2 + 9s + 6 2. s3 + 4s² + 3s С.2 D. 1 Е.4

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Q: 1 Find the inverse transform: F(s) s2+4s+4

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Q: What is the Laplace transform for the function: x(t) = 7te 8t +3. X(s) =

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Q: Given the function Y(0) = S4 Use the Laplace Transform table to convert this function into f(t).

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Q: 8. Find the inverse Laplace transform of the given function: 8s +7 F(s) = s2 +8s + 20

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Q: Given y(t)=t²e+t. The above equation can be transform by using 1. First shift theorem 2. Second…

A: Given  y(t)= t2e4t

Q: 1 Find the inverse transform: F(s) s2-4s+8 1 A. e2t sin 2t C.e2t cos 2t B. e2t sin 2t D. e2t cos 2t

A: The solution of the problem is given in the next step.

Q: Find the inverse Laplace transform f(t) of F(s) = (e-s-e-3s)/(s2

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Q: 3s Find the inverse Laplace transform of the function F(s) = s2 – s – 6 - -

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Q: a) Find the Laplace Transform F(s) of the function. f(t) = (3-e²+ + 56+) sin (7+) 2+

A: The Laplace transform is a mathematical technique used to solve linear ordinary differential…

Q: Find the Laplace transform F(s)= C{S(t)) of the function f(t) = (4- t)(h(t - 3) - h(t - 6)), for s…

A: The Laplace transform of the function f(t) is represented as F(s), and it is defined as…

Q: 3. Find the inverse Laplace transform of F(s) = 180+18,²+354

A: Applying this to each term:  So, the inverse Laplace transform of F(s) is: f(t)=4t6​+43​t4+23​t2…

Q: If the Fourier transform of f(t) = is F(w), express the Fourier transform of g(t) = 2 0<t<1 0…

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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: Compute the inverse Laplace transform: 4s – 2 -5s s2 - s - 6 write u(t-c) for the Heaviside step…

A: We find the given inverse Laplace transform

Q: 5. Find the inverse Laplace transform of the function as + b H(s) : (8 – a)2 + B2"

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Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t)=4e³jt f(t) may be…

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Q: Find the laplace transform of t sin (t) A. 2s/(s2+1)2 B. 1/s2(s2+1) C. 1/s2 + 1/s2+1 D. -…

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Q: Solve the ODE with Laplace transform y(t) = 3 cos(t) + ff y(u)sen(t – u)du

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Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t)=3e²jt f(t) may be…

A: If Fω is the Fourier transform of f(t), then using the linearity property, it can be written that…

Q: Find the inverse Laplace transform of f(t) F(s) = = help (formulas) (Notation: write u(t-c) for the…

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Q: e-t 0くt 2 f(t) :

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Q: Find the Laplace Transform f (x) = 3+2. Answer:

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Q: The non-periodic function f(x) is defined by f(x) = e-l=l. Obtain the Fourier transform of f(x).

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Q: .2 TX e cos(x)

A: Given, fx=e-πx2cosx ∴ℱfx=f~p=12π∫-∞∞eipxfxdx⇒ℱe-πx2cosx=12π∫-∞∞eipxe-πx2cosxdx…

Q: Find the Fourier Transform of the following function f(t): f(t) 1 1.

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