 # RD Sharma Solutions Class 12 Chapter 22 Differential Equations

## RD Sharma Solutions for Class 12 Maths Chapter 22 – Free PDF Download

RD Sharma Solutions for Class 12 Maths Chapter 22 Differential Equations will help you to understand the different forms of differential Equations, their Applications in solving real-life problems like Newton’s law of cooling, problems related to growth and decay, coordinate geometry and more in a very simplified way. Understand all these concepts in detail with complete exercise wise solved RD Sharma Solutions for Class 12 to answer complex problems asked in highly competitive exams like JEE Mains and Advanced accurately.

Further, the RD Sharma Solutions for Class 12 are curated in a stepwise manner for every question in simple language. The primary aim is to provide ease of understanding to students the experts. Referring to these RD Sharma Solutions while solving can increase and strengthen the conceptual knowledge of students. To maximize the possibilities of scoring high marks, solutions are designed according to the latest CBSE guidelines and marling schemes.

### Some important concepts discussed in RD Sharma Class 12 Solutions Chapter 22 Differential Equations

An equation containing a dependent variable, an independent variable and differential coefficients of dependent variable w.r.t. the independent variable is known as a differential Equation.

General Form of a Differential Equation:

$$\begin{array}{l}\boldsymbol{P_{0}\left ( \frac{d^{n}y}{dx^{n}} \right )\;+\;P_{1}\left ( \frac{d^{n-1}y}{dx^{n-1}} \right )\;+\;P_{2}\left ( \frac{d^{n-2}y}{dx^{n-2}} \right )\;+ \;. \;.\; . \;+ \;P_{n-1}\frac{dy}{dx}+P_{n}y\;=\;Q }\end{array}$$

Examples:

$$\begin{array}{l}\frac{dx}{dy}\;=\;5yx\;,\;\frac{dy}{dx}\;=\;2x^{3} + 12xy\;,\; \frac{dx}{dy}-sin \;x=cos\;x\;,\;\frac{d^{2y}}{dx^{2}}-5x=0\end{array}$$

Order of a Differential Equation:

It is the order of the highest order derivative appearing in the equation.

Examples: The Equation

$$\begin{array}{l}\frac{d^{2}y}{dx^{2}}= 5y+8 \left ( \frac{dy}{dx} \right )^{2}\end{array}$$
is of order 3

The equation

$$\begin{array}{l}\frac{d^{5}y}{dx^{5}}= -6y+15 \left ( \frac{dy}{dx} \right )^{7}\end{array}$$
is of order 5.

Degree of a Differential Equation:

It is the degree of the highest order derivative (Differential coefficients are free from fraction and radicals).

Examples: The Equation

$$\begin{array}{l}\frac{d^{4}y}{dx^{4}}-7y= 10 \left ( \frac{dy}{dx} \right )^{8}\end{array}$$
is of degree 1 because, the power of the highest order derivative in this differential equation is 1.

The Equation

$$\begin{array}{l}\left ( \frac{d^{3}y}{dx^{3}} \right )^{5}= 21y-10 \left ( \frac{dy}{dx} \right )^{2}\end{array}$$
is of degree 5 because, the power of the highest order derivative in this differential equation is 5.