Answer: Homogeneous (degree 1).
- A Exact, requiring a specific test condition
- B Homogeneous (degree 1)
- C Linear, requiring a different solving method
- D Separable, allowing direct variable splitting
Correct answer: B. Homogeneous (degree 1)
Explanation: f(tx, ty) = (tx+ty)/(tx-ty) = t(x+y)/t(x-y) = f(x,y). Degree 1 homogeneous. Substitute y = vx.
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