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The image shows a set of differential equations from a mathematics technical course (Matematika Teknik 2). Here's a transcription of the equations from the image for further analysis and solution:

### Differential Equations:

1. \((x + 2y^2)dx + 2xy \, dy = 0\)
2. \((2x + te^y)dx + x \, e^y \, dy = 0\)
3. \((x + y \cos x)dx + \sin x \, dy = 0\)
4. \((x^2 + 1)dx + (x - 3)dy = 0\)
5. \((3y - 2x) \, t \, dx - (9x - 3y - 2) \, dy = 0\)

These are first-order differential equations that can be approached using methods such as:
- Exact equations
- Integrating factors
- Separation of variables
- Homogeneous and non-homogeneous forms

Would you like a detailed solution for one or more of these equations? Let me know which one you'd like to begin with!

### 5 Related Questions:
1. What are exact differential equations, and how can you solve them?
2. How can you apply the method of integrating factors to solve non-exact equations?
3. What is the significance of homogeneous functions in differential equations?
4. How can separation of variables be used in first-order differential equations?
5. What role does the initial condition play in solving differential equations?

### Tip:
Always check if a differential equation is exact before proceeding, as this can simplify the solving process significantly.

Solve the given differential equations:
1. (x + 2y^2)dx + 2xy dy = 0
2. (2x + te^y)dx + x e^y dy = 0
3. (x + y cos x)dx + sin x dy = 0
4. (x^2 + 1)dx + (x - 3)dy = 0
5. (3y - 2x) t dx - (9x - 3y - 2) dy = 0

Learn how to solve first-order differential equations using methods like exact equations, integrating factors, and separation of variables. Detailed solutions for problems such as (x + 2y^2)dx + 2xy dy = 0 are provided, making this suitable for undergraduate mathematics students.

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