The image contains four problems related to differential equations. Here are the tasks presented:

1. Solve the differential equation:

$(3x^2 + 4xy)dx + (2x^2 + 2y)dy = 0$

2. Solve the initial value problem:

$(2x \cos y + 3x^2 y) dx + (x^3 - x^2 \sin y - y) dy = 0, \quad y(0) = 2$

3. Solve the partial differential equation (PD):

$(3x^2 y^2 - x) dy + (2xy^3 - y) dx = 0$

4. Solve the initial value problem:

$(y^3 + \cos(x + y^2)) dx + (3xy^2 + 2y \cos(x + y^2)) dy, \quad y(0) = 1$

Would you like me to begin solving these problems step by step? If so, which problem would you like to focus on first? Let me know if you'd like to explore any details further.

Here are 5 related questions for further exploration:

1. What is an exact differential equation, and how do we check if an equation is exact?
2. How can integrating factors be used to solve non-exact differential equations?
3. What are the differences between ordinary differential equations and partial differential equations?
4. How does one apply the initial condition to solve a first-order differential equation?
5. What are common methods for solving first-order non-linear differential equations?

Tip: When solving differential equations, always check whether the given equation is exact by calculating partial derivatives of the coefficients.