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📐 Mathematics  ·  Differential Equations  ·  JEE

Solve dy/dx = (x² + y²)/(2xy) (Bernoulli-type homogeneous):

Answer: y² - x² = Cx.

  • A x² - y² = Cx
  • B y² - x² = Cx
  • C y = Cx²
  • D x² + y² = Cx

Correct answer: B. y² - x² = Cx

Explanation: Homogeneous: let y=vx. After substitution and simplification: y² - x² = Cx.

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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