Practice General Form Of A Non-homogeneous Second-order Linear Differential Equation (8.1)

Practice: General Form of a Non-Homogeneous Second-Order Linear Differential Equation

Lesson 8.1Solution by Variation of Parameters

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the general form of a non-homogeneous second-order linear differential equation?
Show hintHide hint
Think about the structure: it includes derivatives and functions.
Question 2.
Identify the dependent variable in the equation.
Show hintHide hint
What do we generally measure or calculate in these equations?
3Question 3.
What is the standard form of a non-homogeneous second-order linear differential equation?
- a) y′′ + p(x)y′ + q(x)y = 0
- b) y′′ + p(x)y′ + q(x)y = g(x)
- c) y′ + p(y)y + q(x) = g(x)
Show hintHide hint
Look for the term that represents external input.
4Question 4.
True or False: The function p(x) represents a non-homogeneous term.
- True
- False
Show hintHide hint
Think about the roles of each variable in the equation.
Question 5.
Solve the equation y′′ + 3y′ + 2y = sin(x) and explain each part of your solution.
Show hintHide hint
Identify each function and consider the application of particular solutions.
Question 6.
Describe how changing g(x) to a polynomial affects the overall solution.
Show hintHide hint
Reflection on the form of g(x) leads to varied methods of finding fields of applications.

4 more questions in this section. Enroll free to practise them all.