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, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation: (-4x2 – 3y)dx + (-3x – 4y²)dy = 0 First: M,(x, y) = -3 and N(x, y) = -3 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, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation: (-4x2 – 3y)dx + (-3x – 4y²)dy = 0 First: M,(x, y) = -3 and N(x, y) = -3 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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What is the exact equation
![**Exact Differential Equation Check**
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, \( dF(x, y) \), is the left-hand side of the differential equation. That is, level curves \( F(x, y) = C \) are solutions to the differential equation:
\[
(-4x^2 - 3y)dx + (-3x - 4y^2)dy = 0
\]
**Steps**
First:
\[ M_y(x, y) = \]
\[ \text{\ \ \ \ \ \ \ \ \ \ \ \ } -3 \]
\[ N_x(x, y) = \]
\[ \text{\ \ \ \ \ \ \ \ \ \ \ \ } -3 \]
If the equation is not exact, enter "not exact," otherwise enter \( F(x, y) \) here:
\[ \text{\ \ \ \ \ \ \ \ \ \ \ \ } \text{(Enter solution here)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc247cb8d-78ad-4f89-a50f-ab06364ea5f4%2F40cc8ad1-9e50-49d7-bfc5-aa97b8c607b7%2F0qcjn9_processed.png&w=3840&q=75)
Transcribed Image Text:**Exact Differential Equation Check**
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, \( dF(x, y) \), is the left-hand side of the differential equation. That is, level curves \( F(x, y) = C \) are solutions to the differential equation:
\[
(-4x^2 - 3y)dx + (-3x - 4y^2)dy = 0
\]
**Steps**
First:
\[ M_y(x, y) = \]
\[ \text{\ \ \ \ \ \ \ \ \ \ \ \ } -3 \]
\[ N_x(x, y) = \]
\[ \text{\ \ \ \ \ \ \ \ \ \ \ \ } -3 \]
If the equation is not exact, enter "not exact," otherwise enter \( F(x, y) \) here:
\[ \text{\ \ \ \ \ \ \ \ \ \ \ \ } \text{(Enter solution here)} \]
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