Laplace Transform of Derivatives - Problem 5 - Laplace Transform - Engineering Mathematics 3

TL;DR

Learn how to solve a third order differential equation by applying Laplace transform, finding the roots of the equation, and using inverse Laplace transform to obtain the solution.

Transcript

do subscribe to lehre China and place bill icon to get updates about latest engineering Jessie and IIT day made and advanced videos and a student so after completing the four problems or glasses from derivative let's move ahead with the next problem in this I am going to take the third order derivative term and we are going to find out the roots of... Read More

Key Insights

• 🔨 Laplace transform is a mathematical tool used to simplify and solve differential equations.
• ❓ By applying Laplace transform to a differential equation, it can be transformed into an algebraic equation.
• ❓ Laplace transform derivative formulas and shifting property are useful in simplifying the equation and finding the solution.
• 🍉 Inverse Laplace transform is used to obtain the solution in terms of the original variable.

Questions & Answers

Q: What is the purpose of applying Laplace transform to differential equations?

Laplace transform is used to simplify differential equations and solve for unknown variables by transforming the equation into an algebraic equation that is easier to handle.

Q: How does Laplace transform help in finding the roots of a differential equation?

The Laplace transform helps in finding the roots of a differential equation by transforming the equation into an algebraic form, allowing for the solution to be obtained through inverse Laplace transform.

Q: What are the steps involved in solving a third order differential equation using Laplace transform?

The steps involved in solving a third order differential equation using Laplace transform include taking the Laplace transform of both sides, applying Laplace transform derivative formulas, simplifying the equation, and using inverse Laplace transform to obtain the solution.

Q: How is the shifting property used in finding the Laplace transform of a function?

The shifting property is used to find the Laplace transform of a function by transforming it into a shifted version of another function, allowing for the computation of the Laplace transform through known formulas.

Summary & Key Takeaways

• The video demonstrates how to solve a third order differential equation using Laplace transform.

• The Laplace transform is applied to both sides of the equation, with each term transformed separately.

• By using Laplace transform derivative formulas and the shifting property, the equation is simplified and the solution is obtained through inverse Laplace transform.