Given the initial conditions x(pi/2)=0 and x'(pi/2)=1 Being the ODE: x''+ x = 0 and its family of solution is x = c1 cos t + c2 sin t Find a solution to the Initial Value Problem

Consider the following fifth-order linear homogeneous initial value problem with constant coefficients: y (5) +y (4)-y'-y=0, y (0)=0, y '(0)=0, y" (0) = 1, y (3) (0)=0, y (4) (0) =0 A B E The solution is given by: y=(1/4) e* + (1/4) e-(1/2) cos(x) The solution is given by: y=(1/4) xe* + (1/8) e*- (3/8) e* + (1/4) cos(x) + (1/4) sin(x) The solution is given by: Ⓒy=(1/8) e¹- (3/8)e*— (1/4) xe¯*+ (1/4) cos(x) - (1/4) sin(x) The solution is given by: y=(1/4).xe*+ (1/8)e- (3/8) e¹+ (1/2) cos(x) + (1/2) sin(x) The solution is given by: y=(1/4) xe* + (1/8) e*- (3/8) e*+ (1/2) cos(x) − (1/2) sin(x)

1. Use Newton-Raphson method to find sixth iteration of a real root of the equation: cosx-xe* =0 with x=1 as initial approximation.

Use imaginary part of the solution to the complexified version of the following ODE to find its particular solution: y"+y-6y=-200 sin(t) Yp =