Answer: dy/dx + y = x (linear in y).
- A dy/dx = y², which is nonlinear due to the squared y term
- B dy/dx + y = x (linear in y)
- C (dy/dx)² = x, nonlinear because the derivative is squared
- D d²y/dx² = y, which is second order, not first order
Correct answer: B. dy/dx + y = x (linear in y)
Explanation: dy/dx + P(x)y = Q(x) is linear first-order. y² or (dy/dx)² makes it nonlinear.
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