Which of the following best defines the general solution of an -order differential…
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Which of the following best defines the general solution of an nth-order differential equation?
(a) A family of functions that contain n+1 independent arbitrary constants and satisfy the differential equation.
(b) Any single function that satisfies both the differential equation and n specified initial conditions.
(c) A family of functions containing exactly n independent arbitrary constants and satisfying the differential equation.
(d) The implicit relation obtained after integrating the differential equation n times without introducing constants.