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📐 Mathematics  ·  Differential Equations  ·  JEE

The integrating factor of the differential equation dy/dx + y = x is:

Answer: e x.

  • A e<sup>x</sup>
  • B e<sup>−x</sup>
  • C x
  • D 1

Correct answer: A. e<sup>x</sup>

Explanation: IF = e<sup>∫P dx</sup> = e<sup>∫1 dx</sup> = e<sup>x.</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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