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CSS Applied Mathematics QUESTION #1324
Question 1
In the variation of parameters method, the Wronskian of two solutions \(y_1\) and \(y_2\) is defined as:
  • \(W=y_1y_2'+y_2y_1'\)
  • \(W=y_1y_2'-y_2y_1'\)✔️
  • \(W=y_1'-y_2'\)
  • \(W=y_1y_2\)
Correct Answer Explanation
The Wronskian of two functions \(y_1\) and \(y_2\) is the determinant of the matrix of the functions and their derivatives: \(W=\begin{vmatrix}y_1&y_2\\y_1'&y_2'\end{vmatrix}=y_1y_2'-y_2y_1'\). If \(W\neq0\) on an interval, \(y_1\) and \(y_2\) are linearly independent.