Consider the pair of functions y₁ = t and y₂ = 3t². Which of these statements are true? Select all that apply. A) W[y₁ , y₂](t) 0 for all values of t in the interval (-2, 2). B) W[y₁ , y₁](t) = 3t² C) The pair y₁ and y₂ constitutes a fundamental set of solutions to some second-order differential equation of the form on the interval (-2, 2). D) Abel's theorem implies that y₁ and y₂ cannot both be solutions of any differential equation of the form on the interval (-2, 2). E) Since there exists a value of t₀ in the interval (-2, 2) for which W[y₁ ,y₂ ](t) = 0, there must exist a differential equation of the form for which the pair y₁ and y₂ constitute a fundamental set of solutions on the interval (-2, 2).

Question

Consider the pair of functions y₁ = t and y₂ = 3t². Which of these statements are true? Select all that apply. A) W[y₁ , y₂](t) > 0 for all values of t in the interval (-2, 2). B) W[y₁ , y₁](t) = 3t² C) The pair y₁ and y₂ constitutes a fundamental set of solutions to some second-order differential equation of the form on the interval (-2, 2). D) Abel's theorem implies that y₁ and y₂ cannot both be solutions of any differential equation of the form on the interval (-2, 2). E) Since there exists a value of t₀ in the interval (-2, 2) for which W[y₁ ,y₂ ](t) = 0, there must exist a differential equation of the form for which the pair y₁ and y₂ constitute a fundamental set of solutions on the interval (-2, 2).

Quizplus · Accepted Answer

The Answer of Consider the pair of functions y₁ = t and y₂ = 3t². Which of these statements are true? Select all that apply. A) W[y₁ , y₂](t) > 0 for all values of t in the interval (-2, 2). B) W[y₁ , y₁](t) = 3t² C) The pair y₁ and y₂ constitutes a fundamental set of solutions to some second-order differential equation of the form on the interval (-2, 2). D) Abel's theorem implies that y₁ and y₂ cannot both be solutions of any differential equation of the form on the interval (-2, 2). E) Since there exists a value of t₀ in the interval (-2, 2) for which W[y₁ ,y₂ ](t) = 0, there must exist a differential equation of the form for which the pair y₁ and y₂ constitute a fundamental set of solutions on the interval (-2, 2).

Consider the Pair of Functions Y1 = T and Y2

Consider the Pair of Functions Y₁ = T and Y₂