Answer: dM/dy = dN/dx.
- A M = N
- B dM/dy = dN/dx
- C M + N = 0
- D dM/dx = dN/dy
Correct answer: B. dM/dy = dN/dx
Explanation: Exactness: partial M/partial y = partial N/partial x (equality of mixed partials).
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