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📐 Mathematics  ·  Differential Equations  ·  JEE

The differential equation whose general solution is y = A cosx + B sinx is:

Answer: y'' + y = 0.

  • A y'' − y = 0
  • B y'' + y = 0
  • C y' + y = 0
  • D y'' + y' = 0

Correct answer: B. y'' + y = 0

Explanation: Differentiating twice gives y'' = −y, i.e. y'' + y = 0.

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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