📐 Mathematics · Differential Equations · JEE

The number of arbitrary constants in the general solution of a second-order differential equation is:

Answer: 2.

Correct answer: A. 2

Explanation: The general solution of an nth-order equation contains n arbitrary constants, so a second-order one has 2.

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 number of arbitrary constants in the general solution of a second-order differential equation is:

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