7 If one root of the characteristic equation to a linear hom

7. If one root of the characteristic equation to a linear homogeneous DE is 3 i, then another root must be D. It is the only root E. None B. 3 8. Suppose a nonhomogeneous DE as a complementary solution o yo C1 4x and g(x) 4x. What would the correct form for the particular solution be when using the method of undetermined coefficients? B. yp Ax+ B D. yp Ax2 Bx C E. None A. yp F Ax

Solution

(7). If one of the charesteristic equation to a linear homogeneous DE is 3+i, the the another root must be conjugate of 3+i

so, the other root= 3-i (B)

(8)Here g(x)=4x whic is a linear expression,

so, the particular solution will be a linear

therefore Yp=Ax+B