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📐 Mathematics  ·  Differential Equations  ·  JEE

The differential equation of the family of lines y = mx (m arbitrary) is:

Answer: dy/dx = y/x.

  • A dy/dx = y/x
  • B dy/dx = x/y
  • C dy/dx = x
  • D dy/dx = 1

Correct answer: A. dy/dx = y/x

Explanation: From y = mx, m = y/x, and dy/dx = m, so dy/dx = y/x.

Family of Solution Curves: y = Ax²Each value of the constant A gives ONE particular curve from the family

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.

Concept context

Equations involving derivatives and their solutions

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