## Preparation for Class 12 with Solutions

## FAQs on RD Sharma Class 12 Solutions Chapter 22 - Differential Equations (Ex 22.10) Exercise 22.10 - Free PDF

**1. What are the types of differential equations?**

**The Differential Equations can be Classified as Follows:**

- Ordinary Differential Equation
- Partial Differential Equation
- Homogeneous Differential Equation
- Non-Homogeneous Differential Equation

**2. What is an ordinary differential equation?**

The “Ordinary Differential Equation”, which is also known as ODE, is an equation that contains only one single independent variable and one or more of its derivatives concerning the variable. Hence, the ordinary differential equation is represented as the relation having the independent variable x, the real dependent variable y, with some of its derivatives y’, y”, ….yn,… concerning x. The ordinary differential equation can be homogeneous or non-homogeneous which are discussed later.

**3. What is a partial differential equation?**

The equation that involves only partial derivatives of one or more functions of two or more independent variables is called a partial differential equation which is also known as PDE. Example:

δu/ dx + δ/dy = 0,

δ2u/δx2 + δ2u/δx2 = 0

**4.What is a homogeneous differential equation?**

A differential equation in which the degree of all of the terms is the same is known as a homogeneous differential equation. They can be written in the form of P(x,y)dx + Q(x,y)dy = 0, where P(x,y) and Q(x,y) are homogeneous functions of the same degree in general.

**5. What is a non-homogeneous differential equation?**

A differential equation in which the degree of all of the terms is not the same is known as a homogeneous differential equation. One of the types of non-homogeneous differential equations is the linear differential equation, which is similar to the linear equation. The differential equation which is given as (dy/dx) + Py = Q (Where P and Q are functions of x) is known as a linear differential equation. (dy/dx) + Py = Q (Where P, Q are constant or functions of y). The general solution of a non-homogeneous equation is y × (I.F.) = ∫Q(I.F.)dx + c where, I.F(integrating factor) = e∫pdx