Answer: All terms with y (and dy) can be separated from terms with x (and dx).
- A The equation is linear in y with constant coefficients throughout
- B All terms with y (and dy) can be separated from terms with x (and dx)
- C The equation is generally nonlinear in both the x and y terms together
- D The order of the differential equation exceeds two in this case
Correct answer: B. All terms with y (and dy) can be separated from terms with x (and dx)
Explanation: Separation of variables: rewrite as f(y)dy = g(x)dx and integrate both sides separately.
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