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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:**
   \[
   (y^3 + \cos(x + y^2)) dx + (3xy^2 + 2y \cos(x + y^2)) dy, \quad y(0) = 1
   \]

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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.

1. Selesaikan persamaan diferensial: (3x^2 + 4xy)dx + (2x^2 + 2y)dy = 0
2. Selesaikan masalah syarat awal: (2xcos y + 3x^2 y)dx + (x^3 - x^2 sin y - y)dy = 0 dengan y(0) = 2
3. Selesaikan PD (3x^2 y^2 - x)dy + (2xy^3 - y)dx = 0
4. Tentukan masalah syarat awal berikut: (y^3 + cos(x + y^2))dx + (3xy^2 + 2ycos(x + y^2))dy, y(0) = 1

Explore the solutions for advanced differential equations and initial value problems, including exact and non-exact equations. This page covers key concepts, such as partial differential equations and integrating factors. Suitable for university-level students.

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