(21) (a) verify that y1(t) : =t and y2(t) :=t3are two

QUESTION:

PROBLEM 27EConsider the linear equation (21) (a) verify that y1(t) : =t and y2(t) :=t3are two solutions to (21) on Furthermore, show that for t0=1.(b) Prove that y1(t) and y2(t) are linearly independent on (c) Verify that the function y3(t) : = |t|3 is also a solution to (21) on (d) Prove that there is no choice of constants c1, c2 such that assumption leads to a contradiction.](e) From parts (c) and (d), we see that there is at least one solution to (21) on that is not expressible as a linear combination of the solutions y1(t),y2(t) . Does this provide a counterexample to the theory in this section? Explain