Answer: x² + xy + y² = C.
- A x² + xy + y² = C
- B x² + 2xy + y² = C
- C x² + xy = C
- D Not exact
Correct answer: A. x² + xy + y² = C
Explanation: M=2x+y, N=x+2y. dM/dy=1=dN/dx=1. Exact. Integral: x²+xy+y²=C.
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