Q1 (a): Use the Laplace transform method to solve generalized Abel integral equation u(t) dt , f(x) = , x– t)a 0 < a <1 to get sin an d u(x) : S(x – t)ª-1f(t)dt, 0

Q: Use the chain rule to find dw dt dw dt W = In (√x² + y² + z²), x = 9 sin(t), y = 8 cos(t), z = 5…

A: W=lnx2+y2+z2 x=9 sin(t) y=8 cos(t) z=5 tan(t)

Q: Use the Laplace transform to solve the difference equation 3x(t) — 4x(t − 1) = 1, x(t)=0 for t < 0.

A: Given: The difference equation, 3xt-4xt-1=1, xt=0 for t&lt;0   To solve: The given difference…

Q: Find the coefficients A(w) and B(w) for the Fourier integral for the function f(x)=-e-³¹ if x>0 and…

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Q: . Find the Laplace transform of the function f(t) = 2t + 3 cos(3t) + 4 sin(3t)

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Q: 8. Solve using the Laplace Transform: x" + 4x + 3x = 1 + e -2, x(0) = 0, '(0) = 1.

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Q: 2. (a) Show that gi(t)g2(t) G₁(f) * G₂(f) where denotes convolution and gi(t) = G₁(f), 92(t)=G₂(f).…

A: We start with the time-domain signals and their Fourier transforms:Now, the convolution in the time…

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: d2y/dt2+a2y=b sin wt  ( laplace transform )

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Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

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Q: Find the Fourier Transform of f(s) = e-ax= a >0

A: The Fourier transform of a function  is given by :

Q: [a² - x², Find the Fourier transform of f(x)= • 0, and hence 1C. |x| > a evaluate (Sin sint-t cost…

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