Which of the following best describes a particular solution to a first-order…
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Which of the following best describes a particular solution to a first-order differential equation?
(a) It is any function that satisfies the differential equation and includes exactly one arbitrary constant.
(b) It is the unique solution that satisfies both the differential equation and a given initial condition, so no arbitrary constants remain.
(c) It is the unique solution that satisfies the differential equation and necessarily passes through the origin.
(d) It is the solution curve for which dxdy=0, i.e. an equilibrium solution of the differential equation.