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Which of the following equations are exact equations? Select all that apply. Do not solve the equations. AR (2x² + 8xy + y²) + (2x² + xy³) dy = 0 6x²y² + 4x³yd = 0 4x + 7y + (3x + 4y) dy=0 da (2x - 2y²) + (12y² - 4xy) dy 0 (3x² + 2xy + 4y²) + (x² + 8xy + 18y) dy = 0

Which of the following equations are exact equations? Select all that apply. Do not solve the equations. AR (2x² + 8xy + y²) + (2x² + xy³) dy = 0 6x²y² + 4x³yd = 0 4x + 7y + (3x + 4y) dy=0 da (2x - 2y²) + (12y² - 4xy) dy 0 (3x² + 2xy + 4y²) + (x² + 8xy + 18y) dy = 0

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter1: Trigonometry
Section: Chapter Questions
Problem 20T: A ball on a spring starts at its lowest point of 6 inches below equilibrium, bounces to its maximum...
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### Determining Exact Equations **Question:** Which of the following equations are exact equations? Select all that apply. Do not solve the equations. 1. \[ (2x^2 + 8xy + y^2) + \left(2x^2 + \frac{1}{3}xy^3 \right) \frac{dy}{dx} = 0 \] 2. \[ 6x^2 y^2 + 4x^3 y \frac{dy}{dx} = 0 \] 3. \[ \boxed{4x + 7y + (3x + 4y) \frac{dy}{dx} = 0} \] 4. \[ (2x - 2y^2) + (12y^2 - 4xy) \frac{dy}{dx} = 0 \] 5. \[ (3x^2 + 2xy + 4y^2) + (x^2 + 8xy + 18y) \frac{dy}{dx} = 0 \] Here, we present a list of differential equations for determining which among them are exact. An equation is exact if the total differential form \( M(x, y) \, dx + N(x, y) \, dy = 0 \) satisfies the condition \[ \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}. \] Let's identify which of the equations meet this criterion. **Graphs/Diagrams Explanation:** There are no graphs or diagrams included in the image. The provided content consists solely of differential equations that require analysis to determine their exactness according to the given criteria of partial derivatives.
Transcribed Image Text:### Determining Exact Equations **Question:** Which of the following equations are exact equations? Select all that apply. Do not solve the equations. 1. \[ (2x^2 + 8xy + y^2) + \left(2x^2 + \frac{1}{3}xy^3 \right) \frac{dy}{dx} = 0 \] 2. \[ 6x^2 y^2 + 4x^3 y \frac{dy}{dx} = 0 \] 3. \[ \boxed{4x + 7y + (3x + 4y) \frac{dy}{dx} = 0} \] 4. \[ (2x - 2y^2) + (12y^2 - 4xy) \frac{dy}{dx} = 0 \] 5. \[ (3x^2 + 2xy + 4y^2) + (x^2 + 8xy + 18y) \frac{dy}{dx} = 0 \] Here, we present a list of differential equations for determining which among them are exact. An equation is exact if the total differential form \( M(x, y) \, dx + N(x, y) \, dy = 0 \) satisfies the condition \[ \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}. \] Let's identify which of the equations meet this criterion. **Graphs/Diagrams Explanation:** There are no graphs or diagrams included in the image. The provided content consists solely of differential equations that require analysis to determine their exactness according to the given criteria of partial derivatives.
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