Answer: y = cosh(2x).
- A y = cosh(2x)
- B y = e<sup>2x</sup> + e<sup>-2x</sup>
- C y = cos(2x)
- D y = sinh(2x)
Correct answer: A. y = cosh(2x)
Explanation: Auxiliary: m² = 4, m = ±2. y = Ae<sup>2x</sup> + Be<sup>-2x</sup>. y(0)=A+B=1, y'(0)=2A-2B=0 so A=B=1/2. y = (e<sup>2x</sup>+e<sup>-2x</sup>)/2 = cosh(2x).
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