just c-e, please!please thoroughly explain, because current explanations for these answers on this site don't exactly make sense to me. Label each of the following statements as true or false. If true, prove the statement. If false,provide a counterexample.(a) If the characteristic equation of a constant-coefficient, linear, homogeneous ODE has onenon-real root, then it has at least two non-real roots.(b) Let a, b, c, xo, x1, Yo, Y1 ER and xo # Yo, a # 0. Then the ODE ay" + by' + cysatisfying y(xo)= yo and y'(x1)Yı is guaranteed a unique solution.(c) Let p and q be polynomials of degree n with domain R. If there exists cER such thatW [p, q](c) = 0, then p and q are linearly dependent.(d) Suppose the general solution of a linear, second-order ODE is y =domain D, where C1, C2 E R. Then for any x e D, W[yl, y2](x) # 0.C141 + C2y2 with(e) Let L denote the Laplace transform and f (t) =sin(t)cos(t)Then L(f) exists.

To find: Whether the given statement is true or false.

Answered: Let p and q be polynomials of degree n…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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