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📐 Mathematics  ·  Differential Equations  ·  JEE

The DE dy/dx = (x + y)/(x - y) is:

Answer: Homogeneous (degree 1).

  • A Exact, requiring a specific test condition
  • B Homogeneous (degree 1)
  • C Linear, requiring a different solving method
  • D Separable, allowing direct variable splitting

Correct answer: B. Homogeneous (degree 1)

Explanation: f(tx, ty) = (tx+ty)/(tx-ty) = t(x+y)/t(x-y) = f(x,y). Degree 1 homogeneous. Substitute y = vx.

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

Read the full Differential Equations notes →