6.1 - General Form of a Linear Non-Homogeneous Differential Equation
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.
Practice Questions
Test your understanding with targeted questions
What is the general form of a second-order linear non-homogeneous differential equation?
💡 Hint: Look for the terms that indicate the order and type.
Define a complementary function.
💡 Hint: Think about the solution when the right side of the equation is zero.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is a key distinguishing feature of a non-homogeneous differential equation?
💡 Hint: Consider what distinguishes these types of equations.
True or False: The complementary function describes the natural response of the system.
💡 Hint: Think about the context of a homogeneous equation.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
Derive both the complementary function and particular integral for the equation $$ y'' + 4y' + 4y = e^{-2x} $$, and explain the significance of each part.
💡 Hint: Start with the characteristic equation for the CF and derive the correct guess for the PI.
Using the method of variation of parameters, solve the equation $$ y'' + y = cos(t) $$.
💡 Hint: Ensure you use the correct form and accounts for the coefficients in your calculations.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.