Answer: y = (A+Bx)e²ˣ.
- A y = Ae²ˣ
- B y = (A+Bx)e²ˣ
- C y = A cos 2x + B sin 2x
- D y = Ae²ˣ + Be<sup>-2x</sup>
Correct answer: B. y = (A+Bx)e²ˣ
Explanation: Repeated root m: CF = (A + Bx)e<sup>mx</sup>. For m=2: y = (A+Bx)e²ˣ.
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