The **general solution** of a differential equation contains:
ANo arbitrary constants
BAs many arbitrary constants as the order of the equation
CExactly one arbitrary constant always
DMore constants than the order of the equation
Answer & Solution
Correct answer: B. As many arbitrary constants as the order of the equation
An $n$-th order DE has a general solution with $n$ arbitrary constants.
Particular solutions arise when constants are fixed by initial/boundary conditions.
Keep practising Unit 7: Differential Equations and Modeling
Browse all Unit 7: Differential Equations and Modeling questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
Mode of {1, 2, 2, 3, 4, 4, 4, 5}:A matrix with all elements zero is called:arccos(x) + arccos(-x) =Simplify arctan(sin x / (1+cos x)) for x ∈ (-π, π):Value of arctan(1):Number of rows in matrix A times number of columns in A x B should equal:The half-life of a radioactive substance decaying by $dm/dt = -km$ (with $k > 0$) in termsSolve $\dfrac{dy}{dx} = \dfrac{y + qrt{x^2 + y^2}}{x}$.