Answer: y = vx.
- A y = vx
- B y = x + v
- C v = x/y
- D y = x²
Correct answer: A. y = vx
Explanation: Substitute y = vx (so dy/dx = v + x dv/dx). Transforms homogeneous DE to separable form.
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