Answer: e x and e 2x.
- A e<sup>x</sup> and e<sup>2x</sup>
- B e<sup>3x</sup>
- C sin x and cos x
- D e<sup>-x</sup> and e<sup>-2x</sup>
Correct answer: A. e<sup>x</sup> and e<sup>2x</sup>
Explanation: Auxiliary: m² - 3m + 2 = 0, (m-1)(m-2) = 0. m = 1, 2. CF = Ae<sup>x</sup> + Be<sup>2x</sup>.
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