Practice Advanced Extension: Higher-order Equations (7.11) - Solution by Undetermined Coefficients
Students

Academic Programs

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

Engineering Courses
Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Certifications
Games

Interactive Games

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

Advanced Extension: Higher-Order Equations

Practice - Advanced Extension: Higher-Order 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

Write the general form of a higher-order linear differential equation.

💡 Hint: Think about how the highest derivative is represented.

Question 2 Easy

What is the complementary function?

💡 Hint: Remember, it excludes the non-homogeneous part.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the standard form of a higher-order linear ODE?

a) y'' + b = 0
b) \\frac{d^n y}{dx^n} + a_{n-1}\\frac{d^{n-1}y}{dx^{n-1}} + \\cdots + a_0y = f(x)
c) y + a = 0

💡 Hint: Consider how derivatives are arranged in an equation.

Question 2

True or False: The method of undetermined coefficients can be applied to any type of function.

True
False

💡 Hint: What types of functions are typically used?

Get performance evaluation

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Solve the equation y^(4) + 2y^(3) - y' = sin(x) e^(2x). Find both the complementary and particular solutions.

💡 Hint: What are the characteristic roots of the homogeneous part?

Challenge 2 Hard

Consider the mixed forcing function f(x) = x^4 + cos(3x). What would be your steps and trial solutions for this higher-order ODE?

💡 Hint: Make sure to list all component functions!

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.