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.