Which of the following equations are exact equations? Select all that apply. Do not solve the equations. dy (2x² + 8xy + y²) + (2x² + xy³)² = 0 3 6x²y² + 4x³ydy = 0 panes dy 4x + 7y + (3x + 4y) d=0 CUTTID (2x - 2y²) + (12y² - 4xy) dy dx ******** 0 dy (3x² + 2xy + 4y²) + (x² + 8xy + 18y) d XEMEN 0 HEMMISTONDA

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 17E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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### Exact Equations Identification

**Task:**
Determine which of the following differential 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. \[4x + 7y + (3x + 4y) \frac{dy}{dx} = 0\]

4. \[(2x - 2y^2) + (12y^2 - 4xy) \frac{dy}{dx} = 0\]

5. \[(3x^2 + 2xy + 4y^2) + (x^2 + 8xy + 18y) \frac{dy}{dx} = 0\]

Among these, one equation has been highlighted for clarity:

- Equation (3) \(4x + 7y + (3x + 4y) \frac{dy}{dx} = 0\) is highlighted.

Select the equations that are exact based on the given list.
Transcribed Image Text:### Exact Equations Identification **Task:** Determine which of the following differential 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. \[4x + 7y + (3x + 4y) \frac{dy}{dx} = 0\] 4. \[(2x - 2y^2) + (12y^2 - 4xy) \frac{dy}{dx} = 0\] 5. \[(3x^2 + 2xy + 4y^2) + (x^2 + 8xy + 18y) \frac{dy}{dx} = 0\] Among these, one equation has been highlighted for clarity: - Equation (3) \(4x + 7y + (3x + 4y) \frac{dy}{dx} = 0\) is highlighted. Select the equations that are exact based on the given list.
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,