Suppose that the Wronskian of two functions f_1(t) and f_2(t) is given by W(t) =

Question

Suppose that the Wronskian of two functions f_1(t) and f_2(t) is given by

W(t) = t^2-4 = det f_1(t) f_2(t)
( )
f'_1(t) f'_2(t)

Even though you don't know the functions f_1 and f_2 you can determine whether the following questions are true or false.

1. There is some second order, linear, homogeneous equations satisfied by both functions f_1 and f_2

2. The vectors (f_1(4) ,f_1'(4) ) and (f_2(4) ,f_2'(4) ) are linearly independent

3. The vectors (f_1(0) ,f_1'(0) ) and (f_2(0) ,f_2'(0) ) are linearly independent

4. The vectors (f_1(-2) ,f_1'(-2) ) and (f_2(-2) ,f_2'(-2) ) are linearly independent

5. The equations af_1(2)+bf_2(2) = c
af'_1(2)+bf'_2(2) = d

have a unique solution for any c and d

Explanation / Answer

(1) first answer is wrong. Since wronskian of y1, y2 i.e. W(y1, y2)(x) is either identically zero or never zero. But here t^2-4 is zero for t=2 and nonzero for t=1. so there is no second order linear homogeneous equation which satisfy above wronskian. So first option is FALSE.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.