Answer: y = ax + b (linear).
- A y = constant
- B y = ax + b (linear)
- C y = x²
- D y = e<sup>x</sup>
Correct answer: B. y = ax + b (linear)
Explanation: Integrate twice: dy/dx = A (constant). y = Ax + B. Linear function.
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