Answer: CF + PI (complementary function + particular integral).
- A Just the particular integral, with little homogeneous contribution
- B Just the complementary function, mostly ignoring the forcing term
- C CF + PI (complementary function + particular integral)
- D The product of the complementary function and particular integral
Correct answer: C. CF + PI (complementary function + particular integral)
Explanation: Complete solution = CF (solution of homogeneous part, with n constants) + PI (one particular solution of non-homogeneous part).
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