Answer: Non-homogeneous linear DE when particular integral cannot be guessed.
- A First-order equations specifically, regardless of homogeneity status
- B Non-homogeneous linear DE when particular integral cannot be guessed
- C Exact equations specifically, where an integrating factor already exists
- D Separable equations where the variables split cleanly apart
Correct answer: B. Non-homogeneous linear DE when particular integral cannot be guessed
Explanation: Variation of parameters: powerful method for finding particular integral of non-homogeneous linear DE, especially when RHS has non-standard forms.
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