Practice Laplace Transform in Solving Differential Equations - 15.14 | 15. Fourier Integral to Laplace Transforms | Mathematics (Civil Engineering -1)
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Laplace Transform in Solving Differential Equations

15.14 - Laplace Transform in Solving Differential Equations

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the general form of a second-order linear ODE?

💡 Hint: Look for coefficients and derivatives in the equation.

Question 2 Easy

What does the Laplace Transform do?

💡 Hint: Think about transformations that simplify solving equations.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the Laplace Transform of y''?

s^2Y(s) + sy(0) + y'(0)
s^2Y(s) - sy(0) - y'(0)
Y(s) + y(0)

💡 Hint: Focus on how derivatives are represented in the transform.

Question 2

True or false: The Laplace Transform can only be applied to periodic functions.

True
False

💡 Hint: Think about the broader applicability of the transform in different conditions.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider the equation y'' + 4y = sin(t), with initial conditions y(0) = 1 and y'(0) = 0. Apply the Laplace Transform and find Y(s).

💡 Hint: Focus on how sin(t) transforms and how to handle initial values.

Challenge 2 Hard

Find the inverse Laplace Transform of Y(s) = 5/(s^2 + 1).

💡 Hint: Remember the transformation pairings for sine functions.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.