Answer: The dependent variable and all its derivatives appear with power 1.
- A The dependent variable and all its derivatives appear with power 1
- B First-order derivatives specifically are present, regardless of their powers
- C The independent variable x appears, with y largely absent from the expression
- D All the coefficients multiplying the derivatives are constants
Correct answer: A. The dependent variable and all its derivatives appear with power 1
Explanation: Linear DE: dependent variable (y) and all its derivatives appear with power 1. No products like y × y', etc.
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