Allied & ICAR Exam Bank • ALLIED_2709 MCQ • 1 Mark

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Higher order linear ODEs with constant coefficients

Question Statement:

In the method of variation of parameters for $y'' + P y' + Q y = R$, the Wronskian $W(y_1, y_2)$ is defined as:

Options:

  • (A) $y_1 y_2' - y_1' y_2$
  • (B) $y_1 y_2' + y_1' y_2$
  • (C) $y_1' y_2' - y_1 y_2$
  • (D) $y_1 / y_2$

Answer Key:

A

Step-by-Step Solution & Explanation

The Wronskian is the determinant of the fundamental matrix: $W = \begin{vmatrix} y_1 & y_2 \\ y_1' & y_2' \end{vmatrix} = y_1 y_2' - y_1' y_2$.
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