(1 point) 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, and f. yp(x)=e3x(acos2x+bsin2x) 1. f d2ydx2+4y=x−x220 2. b d2ydx2+6dydx+8y=e2x 3. c y′′+4y′+13y=3cos2x 4. d 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
For each of the yp(x) we can deduce the characteristic polynomial of the differential equation
hope this helps!!
ok so the answer to your question is simple as long as you look at the different dimensions that contain the exemplary letters that combined in the right order give you words that eventually within the 5th dimension will conform and give you the correct answer to your question. hope i , stop looking at this easily, look at it with a spectral view.