Example of First-Order Differential Equation

First-Order Differential Equation

The first-order differential equation is defined by an equation: dy/dx = f(x, y). It involves two variables x and y, where the function f(x, y) is defined on a region in the xy-plane. For any linear expression in y, the first-order differential equation [Tex]y’ = f (x, y)[/Tex] is linear. Nonlinear differential equations are those that aren’t linear....

Example of First-Order Differential Equation

Some examples of first-order differential equation...

Types of First-Order Differential Equation

First-order differential Equations are classified into several forms, each having its characteristics. Types of the First-Order Differential Equations:...

First-Order Differential Equation Solution

First-Order Differential Equation is generally solved and simplified using two methods mentioned below....

Properties of First-Order Differential Equation

Various properties of linear first-order differential equation are:...

First-Order Differential Equation Formulas

[Tex]\begin{array}{|c|c|c|} \hline \textbf{Type of Equation} & \textbf{General Form} & \textbf{Solution Method} \\ \hline \text{Linear Differential Equations} & \frac{dy}{dx} + p(x)y = q(x) & \text{Use an integrating factor, } \mu(x) = e^{\int p(x) \, dx}, \text{ then solve } \frac{d}{dx}(\mu(x)y) = \mu(x)q(x). \\ \hline \text{Homogeneous Equations} & \frac{dy}{dx} = f\left(\frac{y}{x}\right) & \text{Make the substitution } v = \frac{y}{x}, \text{ then solve the resulting separable differential equation for } v. \\ \hline \text{Exact Equations} & M(x,y) + N(x,y)\frac{dy}{dx} = 0 & \text{Find a potential function } \Psi \text{ such that } d\Psi = Mdx + Ndy, \text{ where } \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}. \\ \hline \text{Separable Equations} & \frac{dy}{dx} = g(x)h(y) & \text{Separate variables and integrate: } \int \frac{1}{h(y)} dy = \int g(x) dx + C. \\ \hline \text{Integrating Factor} & \text{Often used for non-exact linear equations} & \text{Find an integrating factor } \mu(x) \text{ that makes the equation exact, then proceed as with exact equations.} \\ \hline \end{array} [/Tex]...

Applications of First-Order Differential Equation

Numerous disciplines, including physics, engineering, biology, economics, and more, first-order differential equations are used. Among other things, they are used to simulate phenomena like fluid dynamics, electrical circuits, population dynamics, and chemical reactions. Various applications of the first-order differential equation are:...

First Order Differential Equation Examples with Solution

Below are the example of problems on First Order Differential Equation....

First Order Differential Equation Questions

Q1: For differential equation dy/dx + yx2 = sin x find integrating factor....

First Order Differential Equation FAQs

What is First Order Differential Equation?...