Please EXPLAIN!! (5 points) Let y1(x),y2(x) and y3(x) be three solutions of the
ID: 3124147 • Letter: P
Question
Please EXPLAIN!!
(5 points) Let y1(x),y2(x) and y3(x) be three solutions of the homogeneous equation y''' +3y'' +5yy'- 4y = 0
and let y(x) be defined as
y(x) = c1y1(x) + c2y2(x) + c3y3(x)
Consider the statements:
I: y(x) is a general solution of the given equation if y1(x),y2(x) and y3(x) are linearly independent.
II: y(x) is a general solution of the given equation if the Wronskian of y1(x),y2(x) and y3(x) is not zero.
III: y(x) is a general solution of the given equation if y1(x),y2(x) and y3(x) form a fundamental set of solutions. IV: y(x) is a general solution of the given equation if y1(x),y2(x) and y3(x) are not multiples of each other.
Which of these statements is true? (A) All of them are true.
(B) None of these choices is correct. (C) II
(D) II and III
(E) I, II and III
Explanation / Answer
I: y(x) is a general solution of the given equation if y1(x),y2(x) and y3(x) are linearly independent.
II: y(x) is a general solution of the given equation if the Wronskian of y1(x),y2(x) and y3(x) is not zero.
III: y(x) is a general solution of the given equation if y1(x),y2(x) and y3(x) form a fundamental set of solutions.
all above three are correct
so answer is:E