please explain all, thanks Fourier Transforms, please explain in detail Solve the following integral equations for...
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Solve the following integral equations for an unknown function f(x): (a) se exp(-at)f (x – t)dt = exp(-bx2) b> a> (b) sono f(t)dt (x-t)2+a? b> a > 0 x2+62 V21
4-6. Using the Fourier transform integral, find Fourier transforms of the following signals: (a) xa(1)-1 exp(-α) u(t), α > 0; (b) xb(t) = u(t) u(1-t);
3. Solve the following integral equations using Laplace transforms. (a) (t)= te! - 2e x(u)e"du (b) y(t) 1 - sinht +(1+T)y(t - T)dT. netions
3. Solve the following integral equations using Laplace transforms. (a) (t)= te! - 2e x(u)e"du (b) y(t) 1 - sinht +(1+T)y(t - T)dT. netions
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Solve the following differential equations for an unknown function f(t): (a) df(t) +2f(t) = X(0,2](t) (b) Sketch the solution for f(t) for 0 <t< 4. dt
(a) Find the Fourier transform of the following function (b) Using Fourier transforms, solve the wave equation , -∞<x<∞ t>0 and bounded as ∞ f(r)e We were unable to transcribe this imageu(r, 0)e 4(r.0) =0 , t ur. We were unable to transcribe this image f(r)e u(r, 0)e 4(r.0) =0 , t ur.
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14. Integral Equations Use Laplace Transforms to solve the integral equation x (t) = 1 ttte (1-T) x (T) dr. jo
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Solve the Cauchy problem for the diffusion equation ut = Uxx, xe (-0, 0), t > 0 (b) u(x,0) = x for x € (-1,1) and u(x,0) = 0 for other values of x.
Solve the system of equations with Laplace Transforms:
(differential equations)
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Solve the system of equations with Laplace Transforms: x' + y' = 1, x(0) = y(0) = x'(0) = y'(0) = 0. y" = x' Let X(s) = LT of x(t) and Y(s) = LT of y(1). First obtain expressions for X(s) and Y(s) and list them in the form ready for obtaining their inverses. a. Y(s) = X(s) = %3D b. Now obtain the inverse transforms....
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ft) satisfies the integral equation: CO Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax. f(t)- Skipped
ft) satisfies the integral equation: CO Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax. f(t)- Skipped
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from Definition)- For (c) r(t) = te-2, 11(1) (b) x(t)-2t rect(t)
1) (Fourier Transforms each of the following signals (a - c), sketch the signal x(t), and find its Fourier Transform X(f) using the defining integral (rather than "known" transforms and properties) (a)x(t) rectt 0.5) from...