alleryFor DE M(x,y) dx + N(x,y) dy = 0 to be EXACT:
AAlways M = N
BLinear
C∂M/∂y = ∂N/∂x (exactness condition)
DM + N = 0
Answer & Solution
Correct answer: C. ∂M/∂y = ∂N/∂x (exactness condition)
**Exact DE:** ∂M/∂y = ∂N/∂x.
Then ∃ F(x,y) with dF = M dx + N dy, solution F(x,y) = C. If not exact, find integrating factor.
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 $\dfrac{dy}{dx} = \dfrac{y + qrt{x^2 + y^2}}{x}$.