Practice Exercises (2.9) - Homogeneous Linear Equations of Second Order

Practise this section

9 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
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Solve the equation d²y/dx² + 5y = 0. What type of roots do you expect?
Show hintHide hint
Use the auxiliary equation.
Question 2.
What is the general solution when you have real distinct roots?
Show hintHide hint
Recall the roots format.
3Question 3.
What form does a second-order linear homogeneous ODE take?
- dy/dx + py + q = 0
- d²y/dx² + p dy/dx + qy = 0
- d²y/dx² = 0
Show hintHide hint
Identify the equality to zero.
4Question 4.
Does the general solution of a second-order ODE have arbitrary constants?
- True
- False
Show hintHide hint
Think about the roots of the auxiliary equation.
Question 5.
Given the equation d²y/dx² + 10 = 0, derive the solution and determine the type of roots.
Show hintHide hint
Convert the equation into auxiliary form.
Question 6.
For d²y/dx² + 8dy/dx + 16y = 0, prove that the roots are repeated and write the general solution.
Show hintHide hint
Look at the discriminant to confirm root multiplicity.

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