Answer: cos 2x frequency matches the homogeneous solution frequency (2).
- A The frequency on the right side happens to match some particular value
- B cos 2x frequency matches the homogeneous solution frequency (2)
- C The coefficient of y in the equation happens to equal 4
- D The equation is second order, which often happens to involve resonance
Correct answer: B. cos 2x frequency matches the homogeneous solution frequency (2)
Explanation: Resonance: forcing frequency equals natural frequency. Homogeneous solution has cos 2x, same as forcing. PI requires extra factor x: y<sub>P</sub> = x(A cos 2x + B sin 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