Answer: dM/dy = dN/dx.
- A M = N
- B dM/dx = dN/dy
- C dM/dy = dN/dx
- D M + N = 0
Correct answer: C. dM/dy = dN/dx
Explanation: Exactness condition: partial derivative of M with respect to y = partial derivative of N with respect to x.
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