Practice Homogeneous Linear Equations With Constant Coefficients (2.2) - Homogeneous Linear Equations of Second Order

Practice: Homogeneous Linear Equations with Constant Coefficients

Lesson 2.2Homogeneous Linear Equations of Second Order

Practise this section

10 questions

Flashcard drill
4 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
4 questions · about 3 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Solve the equation: $\frac{d^2y}{dx^2} + 7\frac{dy}{dx} + 12y=0$ .
Show hintHide hint
Start with the auxiliary equation.
Question 2.
What is the general form of a second-order linear homogeneous equation?
Show hintHide hint
Recall the definition of the equation.
3Question 3.
What characterizes a homogeneous linear equation?
- It has constant coefficients.
- It equals a non-zero constant.
- All terms are linear.
- Both 1 and 3.
Show hintHide hint
Reflect on the definition.
4Question 4.
True or False: The general solution of a second-order linear homogeneous ODE contains three arbitrary constants.
- True
- False
Show hintHide hint
Recall the number of roots affecting the solution.
Question 5.
Solve the differential equation: $\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 6y = 0$ . Determine the nature of the roots and interpret the solution.
Show hintHide hint
Look for factors of the characteristic equation.
Question 6.
Consider the system described by $\frac{d^2y}{dx^2} + 2y = 0$ . Find its general solution and discuss what this means in terms of oscillation.
Show hintHide hint
Recall how complex numbers relate to oscillatory behavior.

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