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The image is related to differential equations, and the question asks which equation is not exact, based on the general form \(A(x, y)dx + B(x, y)dy = 0\).

To determine whether a differential equation is exact, you must check if the following condition holds:
\[
\frac{\partial A}{\partial y} = \frac{\partial B}{\partial x}
\]
Where:
- \( A(x, y) \) is the function multiplying \( dx \)
- \( B(x, y) \) is the function multiplying \( dy \)

The four options shown in the image provide different equations. You need to apply this test to each of them to see which one is not exact.

Would you like a step-by-step solution to each option, or do you want help with a specific one? Let me know if you need further assistance.

Here are 5 related questions to deepen your understanding:
1. What does it mean for a differential equation to be exact?
2. How do you find an integrating factor for non-exact equations?
3. Can a non-exact equation be transformed into an exact one?
4. What are the applications of exact differential equations in real life?
5. How do boundary conditions influence the solution of exact differential equations?

**Tip:** Always remember to cross-check partial derivatives carefully when testing for exactness to avoid calculation errors.

A differential equation of first order is given in the form A(x, y)dx + B(x, y)dy = 0. The question asks: 'Which of the following differential equations is NOT exact?'

Learn how to determine if a first-order differential equation is exact by checking the condition ∂A/∂y = ∂B/∂x. This problem involves checking four different equations and finding which one is not exact, a key concept in differential equations at the undergraduate level.

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