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Linear Differential Equations

Linear Differential Equations

Introduction :  A linear differential equation is an equation with a variable, its derivative, and a few other functions. Linear differential equations with constant coefficients are widely used in the study of electrical circuits, mechanical systems, transmission lines, beam loading, strut and column displacement, shaft whirling, and other topics. Let’s learn about linear differential equations in-depth.

Linear Differential Equations Definition

The linear polynomial equation, which consists of derivatives of several variables, defines a linear differential equation. When the function is dependent on variables and the derivatives are partial, it is also known as Linear Partial Differential Equation.

The expression for a general first-order differential equation is:

Non-Linear Differential Equations: A nonlinear differential equation is defined as the equation in which the unknown function and its derivatives are not linear.

We can use a formula to solve a linear differential equation, a common type of differential problem. Let’s learn how to obtain the general solution of a linear differential equation using the formula and derivation.

Formula for General Solution of Linear Differential Equations

The two important formulas for finding the general solution of linear differential equations are as follows.

Steps To Solve Linear Differential Equations

 The general solutions of a linear differential equation can be written using the three easy steps given below.

The application of the above steps can be understood by solving some of the problems based on linear differential equations.

 

Let’s discuss  solved problems on Linear differential equations.

Shabanam  Kumari

 Assistant Professor

 Department of mathematics

 Email –id : shabu0000sharma@gmail.com