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The Wronskian of two solutions y₁ and y₂ of a 2nd order linear homogeneous DE is W = y₁y₂' - y₁'y₂. If W ≠ 0, the solutions are:

Answer: Linearly independent.

A Identical
B Linearly dependent
C Linearly independent
D Imaginary

Correct answer: C. Linearly independent

Explanation: Wronskian test: W ≠ 0 implies y₁ and y₂ are linearly independent (form a fundamental set of solutions).

The general solution y=Ax² represents an entire FAMILY of curves, one for each value of the arbitrary constant A; a particular solution (fixed by an initial condition) selects exactly one curve from this family.

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Equations involving derivatives and their solutions

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The Wronskian of two solutions y₁ and y₂ of a 2nd order linear homogeneous DE is W = y₁y₂' - y₁'y₂. If W ≠ 0, the solutions are:

Concept context

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