Answer: y = A sinx + B cosx.
- A y = A sinx + B cosx
- B y = Ae<sup>x</sup> + Be<sup>-x</sup>
- C y = (A+Bx)e<sup>x</sup>
- D y = Ae<sup>ix</sup>
Correct answer: A. y = A sinx + B cosx
Explanation: Auxiliary: m² = -1, m = ±i. CF for complex roots ±αi: y = A cos(αx) + B sin(αx). Here α=1.
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