allerySolve d²y/dx² + y = 0 (SHM):
Ay = e^x
By = A cos x + B sin x (or A sin(x + φ))
Cy = x²
Dy = ln x
Answer & Solution
Correct answer: B. y = A cos x + B sin x (or A sin(x + φ))
**Auxiliary equation:** m² + 1 = 0 → m = ±i.
**General solution:** y = A cos x + B sin x.
Two-parameter family (2nd-order needs 2 conditions).
Equation of simple harmonic motion.
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 $\dfrac{dy}{dx} = \dfrac{y + qrt{x^2 + y^2}}{x}$.