https://file.aiquickdraw.com/mathbot/file/1728907386345s2hp0s1f.jpg

The equation in the image is a first-order differential equation:

\[
\frac{dy}{dx} = xy - 3x - 2y + 6
\]

This is a non-linear ordinary differential equation involving both \(x\) and \(y\). One approach to solving this would be to attempt a method like separation of variables (if possible), integrating factor method, or another suitable technique depending on how the equation simplifies.

Would you like me to help you solve this differential equation step by step or try a specific method? Let me know how you'd like to proceed!

### Related Questions:
1. What are the different methods for solving first-order differential equations?
2. Can this differential equation be solved using an integrating factor?
3. How does one approach non-linear differential equations?
4. What conditions or solutions are common in equations involving both \(x\) and \(y\)?
5. What real-world phenomena could be modeled by such a differential equation?

### Tip:
For solving differential equations, always first check if it's separable, linear, or exact before choosing an appropriate solving method.

Solve the first-order differential equation: dy/dx = xy - 3x - 2y + 6

Learn how to solve the first-order non-linear differential equation dy/dx = xy - 3x - 2y + 6. This problem involves methods like separation of variables or using an integrating factor. Suitable for advanced undergraduate students studying differential equations.

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