Answer: y² - x² = Cx.
- A x² - y² = Cx
- B y² - x² = Cx
- C y = Cx²
- D x² + y² = Cx
Correct answer: B. y² - x² = Cx
Explanation: Homogeneous: let y=vx. After substitution and simplification: y² - x² = Cx.
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