Answer: y = Ae²ˣ + Be³ˣ.
- A y = Ae²ˣ + Be³ˣ
- B y = (A+Bx)e²ˣ
- C y = A sin 2x + B cos 3x
- D y = Ae<sup>x</sup> + Be<sup>6x</sup>
Correct answer: A. y = Ae²ˣ + Be³ˣ
Explanation: Two distinct real roots m₁=2, m₂=3: y = Ae<sup>m₁x</sup> + Be<sup>m₂x</sup> = Ae²ˣ + Be³ˣ.
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