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LearnEdge Differential Equations

Name: LearnEdge Differential Equations
SKU: 219
Price: 700 INR
Availability: InStock

Differential Equations are mathematical equations that involve functions and their derivatives. These equations describe how a quantity changes over time or space, and they play a crucial role in modeling real-world phenomena in fields like physics, engineering, biology, economics, and many other areas. They allow us to understand how systems evolve dynamically and provide the tools to solve problems involving rates of change.

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A differential equation is an equation that relates a function to its derivatives, which represent the rate of change of that function. The function could be dependent on one or more variables, and the derivatives indicate how the function changes with respect to those variables.

Key Terms:

Function: The quantity that is changing, typically denoted as $y$ $($ $x$ $)$ or $f$ $($ $x$ $)$ , where $x$ is the independent variable.
Derivative: Represents the rate of change of the function. For example, $dydx\frac{dy}{dx}$ $dxdy$ $$ denotes the rate of change of $y$ with respect to $x$ .
Order: The order of a differential equation is the highest derivative in the equation. For example, if the equation involves $d2ydx2\frac{d^2y}{dx^2}$ $dx$ $2$ $d$ $2$ $y$ $$ , it is a second-order differential equation.
Degree: The degree of a differential equation is the power of the highest-order derivative. For example, $d2ydx2+y=0\frac{d^2y}{dx^2} + y = 0$ $dx$ $2$ $d$ $2$ $y$ $$ $+$ $y$ $=$ $0$ is a second-degree equation.