Using z-transform methods, solve the difference equation Yk+2 - 5yk+1 + 6yk = 5 subject to yo = 0, y1 = 1 %3D
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A: Inverse Laplace transform
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- 21.Consider the equation (35) ay′′+by′+cy=0,ay″+by′+cy=0, where a, b, and c are constants with a ≠ 0. In Chapter 3 it was shown that the general solution depended on the roots of the characteristic equation (36) ar2+br+c=0.ar2+br+c=0. a.Transform equation (35) into a system of first-order equations by letting x1 = y, x2 = y′. Find the system of equations x′ = Ax satisfied by x=(x1x2)x=x1x2.The impulse response of a DT system is h[n] = 3^(n-1)u[n] . Calculate the input x[n] which generates an output y[n] = 2^(n-1)u[n-1] using z-transform method.x(0)=4, x(1)=3, x(2)=2, x(3)=1, x(4)=0, x(5)=0 give as, x(n) series ( 0≥ ? ≥ 5 ). a)calculate x(k) with discrete fourier transform coefficients. (step-by-step should be written)
- How do I solve for the third order y''' - 4y''-11y' + 30y = 4e^8t + t^2 using the method of 1. Undetermined Coefficient 2. Variation of Parameter 3. Laplace Transform given that y(0) =0, y'(0) = 0, y''(0)?Use laplace transform to solve the initial value problem; a) y''+y=alpha(t-1/2pi)+alpha(t-3/2pi), y(0)=0,y'(0)=01. Find the natural cubic spline sN (x) passing through the 3 points (xj, yj) given by (0, 2), (2, 3), and (3, 1).Then evaluate sN (1).
- Use laplace transform to find the initial-value problem of the followings; a) y'-y=2cos5t, y(0)=0 b) y''-4y'=6e^3t -3e^-t, y(0)=1, y'(0)=-1A continuous periodic signal x (t) of real value y has a fundamental period of T = 8. The coefficients of the nonzero Fourier series for x (t) are a1 = a-1 = 2, a3 = a * -3 = 4j Express x (t) in the formSolve the initial value problem y'' - 4y = 6 t exp(t) using Laplace transforms. When writing your answer limit yourself to showing (i) the equation for L(y), the Laplace transform; (ii) the partial fraction decomposition; (iii) the antitransforms that finish the problem. initial condition y(0) = y'(0)=0
- Using Laplace transforms, solve the IVP y'' + 4y - 4 = 0 with the initial conditions y(0) = y'(0) = 0.In this laplace transform problem, y'''-27y=f(t); y(0)=y'(0)=y''(0)=0 with the value f(t)={ 30 for 0<=t<5, and for t>=5 If the given solution is, y(t)=V+W e^(3t-15)+Xe^(15/2-3t/2) cos[Y(t-5)]*H(t-Z) What is the value of V,W,X,Y, and Z?Use a LaPlace transform to determine the solution of the following systems with differential equations a) { (d²x/dt²)-6(dy/dt)-7x=0 with { x(0)=0=x'(0) (d²y/dt²)+x=3 y(0)=0=y'(0) answer : image