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The general solution of dy/dx = e<sup>x − y</sup> is:

Answer: e y = e x + C.

  • A e<sup>y</sup> = e<sup>x</sup> + C
  • B e<sup>−y</sup> = e<sup>x</sup> + C
  • C y = e<sup>x</sup> + C
  • D e<sup>y</sup> = e<sup>−x</sup> + C

Correct answer: A. e<sup>y</sup> = e<sup>x</sup> + C

Explanation: Separating: e<sup>y</sup> dy = e<sup>x</sup> dx, integrating gives e<sup>y</sup> = e<sup>x</sup> + C.

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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