Answer: Sinusoids and cosinusoids (trigonometric basis).
- A Taylor polynomials expanded about a single fixed point
- B Sinusoids and cosinusoids (trigonometric basis)
- C Polynomial terms mainly, with few trigonometric components
- D Real exponential terms mainly, with little oscillatory behavior
Correct answer: B. Sinusoids and cosinusoids (trigonometric basis)
Explanation: A periodic function f(x) with period 2L is expressed as f(x)=a₀/2+Σ[aₙcos(nπx/L)+bₙsin(nπx/L)]. Coefficients found by orthogonality of sin/cos. This is an infinite sum of harmonically related sinusoids and cosinusoids.
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