Question: Only The question C please for true or false Consider xy - (x + 1)y'ty = 8(x) Let y1 = er and y2 = x

Only The question C please for true or false

Consider xy" - (x + 1)y'ty = 8(x) Let y1 = er and y2 = x + 1 be two linear independent solutions to the corresponding homogeneous differential equation. Then, a particular solution of the nonhomogeneous problem is given by yp = uj(x)y1 + u2(x)y2, where (a) u'(x) is given by (b) uh(x) is given by (c) Suppose that yp = -+ 2x + 2 is a solution to the nonhomogeneous differential equation. Consider the following statements. (i) 1 + x - x is also a solution to the nonhomogeneous differential equation. (ii) ex + x is also a solution to the nonhomogeneous differential equation. (iii) 3ex -x is also a solution to the nonhomogeneous differential equation. (iv) ex + 1 + x is also a solution to the nonhomogeneous differential equation

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