1. The problem is to identify whether a given differential equation (DE) is an ordinary differential equation (ODE) or a partial differential equation (PDE), and to state its order and degree. 2. **Definitions:** - An **ODE** involves derivatives with respect to a single independent variable. - A **PDE** involves partial derivatives with respect to two or more independent variables. - The **order** of a DE is the highest order derivative present. - The **degree** of a DE is the power of the highest order derivative after the equation is free from radicals and fractions with derivatives. 3. **Example Exercise:** Identify the type, order, and degree of the differential equation: $$y'' + 3y' + 2y = 0$$ 4. **Step 1: Identify if ODE or PDE** - The equation involves derivatives $y''$ and $y'$ with respect to a single variable (usually $x$). - Therefore, it is an **ODE**. 5. **Step 2: Determine the order** - The highest derivative is $y''$, which is the second derivative. - So, the order is **2**. 6. **Step 3: Determine the degree** - The highest order derivative $y''$ appears to the first power. - The equation is free from radicals and fractions involving derivatives. - So, the degree is **1**. **Final answer:** The given differential equation is an **ODE** of order **2** and degree **1**.