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.
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