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📐 Mathematics  ·  Differential Equations  ·  JEE

d²y/dx² = 0 has solution:

Answer: y = ax + b (linear).

  • A y = constant
  • B y = ax + b (linear)
  • C y = x²
  • D y = e<sup>x</sup>

Correct answer: B. y = ax + b (linear)

Explanation: Integrate twice: dy/dx = A (constant). y = Ax + B. Linear function.

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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