alleryThe order of the differential equation obtained by eliminating the arbitrary constants $A$ and $B$ from $y = A e^{3x} + B e^{-3x}$ is:
A1
B2
C3
D4
Answer & Solution
Correct answer: B. 2
Two arbitrary constants ⇒ second-order DE.
Indeed, differentiating twice and eliminating gives $d^2y/dx^2 = 9y$ — order 2.
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 $\dfrac{dy}{dx} = \dfrac{y + qrt{x^2 + y^2}}{x}$.