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📐 Mathematics  ·  Differential Equations  ·  JEE

The integrating factor of dy/dx + 2y = e<sup>x</sup> is:

Answer: e 2x.

  • A e<sup>x</sup>
  • B e<sup>2x</sup>
  • C e<sup>−2x</sup>
  • D 2x

Correct answer: B. e<sup>2x</sup>

Explanation: IF = e<sup>∫2 dx</sup> = e<sup>2x</sup>.

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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