Practice Application to Ordinary Differential Equations (ODEs) - 18.1 | 16. Application to Ordinary Differential Equations (ODEs) | Mathematics - iii (Differential Calculus) - Vol 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

Application to Ordinary Differential Equations (ODEs)

18.1 - Application to Ordinary Differential Equations (ODEs)

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 does the Laplace Transform do?

💡 Hint: Think about the relationship between derivatives and algebra.

Question 2 Easy

How is the initial condition represented in Laplace Transforms?

💡 Hint: Look for the term f(0) in derivative transformations.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the first step in using Laplace Transforms to solve ODEs?

Take the inverse transform
Substitute initial conditions
Take the Laplace transform of both sides

💡 Hint: It's all about moving to the s-domain first.

Question 2

True or False: Laplace Transforms convert time-domain functions into frequency-domain functions.

True
False

💡 Hint: Think about what s represents.

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Solve the third-order ODE: d^3y/dt^3 + 5d^2y/dt^2 + 6dy/dt = e^{-t}, with appropriate initial conditions.

💡 Hint: Focus on breaking down the steps and applying partial fractions where needed.

Challenge 2 Hard

An RLC circuit described by L(d^2i/dt^2) + R(di/dt) + Ci = V(t) is given. Solve for i(t) assuming V(t) is a step input.

💡 Hint: Utilize the known transforms of step functions and derive appropriately.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.