Answer: y = sinx + C cosx.
- A y = cosx + C sinx
- B y = sinx + C cosx
- C y = tanx + C
- D y = secx + C
Correct answer: B. y = sinx + C cosx
Explanation: IF = secx; (y secx)' = sec²x, so y secx = tanx + C, giving y = sinx + C cosx.
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