alleryLinear DE of first order: dy/dx + P(x) y = Q(x). Solution uses:
ATrial and error
BSubstitution
CDirect integration
DIntegrating factor μ = e^(∫P dx) and y × μ = ∫(Q × μ) dx + C
Answer & Solution
Correct answer: D. Integrating factor μ = e^(∫P dx) and y × μ = ∫(Q × μ) dx + C
**Standard linear DE:** multiply both sides by μ = e^(∫P dx).
Then d/dx(μ y) = μ Q. Integrate: μy = ∫μQ dx + C
→ y = (1/μ)[∫μQ dx + C].
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 $\dfrac{dy}{dx} = \dfrac{y + qrt{x^2 + y^2}}{x}$.