Match the following guess solutions yp for the method of undetermined coefficients with the second-order nonhomogeneous linear equations below. A. yp(x)=Ax2+Bx+C,
B. yp(x)=Ae2x,
C. yp(x)=Acos2x+Bsin2x,
D. yp(x)=(Ax+B)cos2x+(Cx+D)sin2x
E. yp(x)=Axe2x,
F. yp(x)=e3x(Acos2x+Bsin2x)
1. d2ydx2+4y=x−x220
2. d2ydx2+6dydx+8y=e2x
3. y′′+4y′+20y=−3sin2x
4. y′′−2y′−15y=3xcos2x

Answer and Step-by-step explanation:

1. Data provided

Now as a non homogeneous part which is

let us assume the computation is

2. Data provided

As a non homogeneous part is , let us assume the computation is

3. Data provided

As a non homogeneous part −3sin(2x), let us assume the computation is

4. Data provided

As a non homogeneous part  3xcos(2x), let us assume the computation is

b. b < 1 might be the correct answer