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📐 Mathematics  ·  Differential Equations  ·  JEE

The integrating factor for dy/dx + Py = Q (P, Q functions of x) is:

Answer: e integral of P dx.

  • A e<sup>integral of Q dx</sup>
  • B e<sup>integral of P dx</sup>
  • C P × Q
  • D 1/P

Correct answer: B. e<sup>integral of P dx</sup>

Explanation: Linear first-order DE: integrating factor = e<sup>integral P dx</sup>. Multiply both sides to make LHS exact.

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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