Problem 3 Based on Laplace Transform of Derivative Property - Engineering Mathematics 3

TL;DR

Learn how to solve a differential equation using Laplace transform and find the value of y in terms of t.

Transcript

hello friends so after covering a numerical on laplace transform derivative let's move ahead with one more numerical where we are gonna solve the differential equation with the help of laplace transform so here we have to solve d y by dt plus 2y plus integral from 0 to t y dt equal to sign it means we have to solve the differential equation and get... Read More

Key Insights

• ❓ Laplace transform is a useful method to solve differential equations.
• ❓ Solving a differential equation involves applying Laplace transform and finding the inverse Laplace transform.
• ❓ The Laplace transform of a derivative can be calculated using a specific formula.
• ❓ The Laplace transform of an integral can be found using a property of Laplace transform.
• ❓ Partial fraction decomposition is used to find the inverse Laplace transform of a function.

Questions & Answers

Q: What is the first step in solving a differential equation using Laplace transform?

The first step is to apply Laplace transform to both sides of the equation.

Q: How is the Laplace transform of a derivative calculated?

The Laplace transform of a derivative is calculated using the property s⋅L{y} - y(0), where L{y} represents the Laplace transform of y(t) and y(0) is the initial condition.

Q: What is the Laplace transform property for integrals?

The Laplace transform property for integrals states that the Laplace transform of ∫[0 to t] y dt is equal to 1/s times the Laplace transform of y.

Q: How do you find the inverse Laplace transform of a function?

To find the inverse Laplace transform of a function, you can use partial fraction decomposition to separate the function into smaller components and then apply the linearity property of inverse Laplace transform.

Summary & Key Takeaways

• The video explains how to solve a differential equation using Laplace transform.

• The first step is to apply Laplace transform to both sides of the equation.

• The video demonstrates the Laplace transform of derivative and integral terms.