Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, d F(x, y) is the hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation (2e* sin(y) – 3y)dx + (-3x + 2e* cos(y))dy = 0 First, if this equation has the form M(x, y)dx + N(x, y)dy = 0: M,(x, y) = , and N(x, y) = If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, d F(x, y) is the hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation (2e* sin(y) – 3y)dx + (-3x + 2e* cos(y))dy = 0 First, if this equation has the form M(x, y)dx + N(x, y)dy = 0: M,(x, y) = , and N(x, y) = If the equation is not exact, enter not exact, otherwise enter in F(x, y) here
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Mixed Partials Check for Exact Differential Equations**
Use the "mixed partials" check to determine if the following differential equation is exact. If it is exact, identify a function \( F(x, y) \) whose differential, \( dF(x, y) \), matches the left-hand side of the differential equation. In other words, the level curves \( F(x, y) = C \) are solutions to the differential equation.
\[
(2e^x \sin(y) - 3y)dx + (-3x + 2e^x \cos(y))dy = 0
\]
Firstly, express the equation in the form \( M(x, y)dx + N(x, y)dy = 0 \):
- \( M_y(x, y) = \) **[Input Box]**
- \( N_x(x, y) = \) **[Input Box]**
If the equation is not exact, enter "not exact"; otherwise, enter the potential function \( F(x, y) \) here:
- **[Input Box]**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc247cb8d-78ad-4f89-a50f-ab06364ea5f4%2F826ab6c2-7932-4c76-b396-7359c5012160%2F0pwkqsu_processed.png&w=3840&q=75)
Transcribed Image Text:**Mixed Partials Check for Exact Differential Equations**
Use the "mixed partials" check to determine if the following differential equation is exact. If it is exact, identify a function \( F(x, y) \) whose differential, \( dF(x, y) \), matches the left-hand side of the differential equation. In other words, the level curves \( F(x, y) = C \) are solutions to the differential equation.
\[
(2e^x \sin(y) - 3y)dx + (-3x + 2e^x \cos(y))dy = 0
\]
Firstly, express the equation in the form \( M(x, y)dx + N(x, y)dy = 0 \):
- \( M_y(x, y) = \) **[Input Box]**
- \( N_x(x, y) = \) **[Input Box]**
If the equation is not exact, enter "not exact"; otherwise, enter the potential function \( F(x, y) \) here:
- **[Input Box]**
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