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