Скачать или смотреть Solving Differential Equations Using Laplace Transform Technique with Examples

Category of Differential Equations:
a. 𝐋𝐢𝐧𝐞𝐚𝐫 :Only contains linear functon of dependent variable
b. 𝐍𝐨𝐧𝐥𝐢𝐧𝐞𝐚𝐫

a. 𝐅𝐢𝐫𝐬𝐭 𝐨𝐫𝐝𝐞𝐫:indicates the highest derivative of the dependent variable
b. 𝐒𝐞𝐜𝐨𝐧𝐝 𝐨𝐫𝐝𝐞𝐫

a. 𝐎𝐫𝐝𝐢𝐧𝐚𝐫𝐲:The dependent variable is only function of one variable
b. 𝐏𝐚𝐫𝐭𝐢𝐚𝐥

a. 𝐇𝐨𝐦𝐨𝐠𝐞𝐧𝐞𝐨𝐮𝐬 : Does not contain isolated constant and isolated function of independent variable. b. 𝐍𝐨𝐧𝐡𝐨𝐦𝐨𝐠𝐞𝐧𝐞𝐨𝐮𝐬

Laplace Transform:
It simplifies the governing equation of the system.
The Laplace transform changes time-domain functions into the complex frequency domain (s-domain) which transforms differential equation to algebraic equation.
Laplace transformation is particularly useful in engineering and physics for analyzing systems that evolve over time, such as electrical circuits, mechanical systems, and control systems.