Differential Equations (2nd Order)

Question 1

What does it mean for a derivative to be linear?

Answer 1

In which y (dependant variable) is to the power of 1

Question 2

What does it mean when an equation is homogeneous?

Answer 2

The RHS =0

Question 3

Answer 3

Question 4

What conditions must the equation have for the auxiliary method to be used?

Answer 4

Linear and homogeneous and constant coefficients

Question 5

Using the auxiliary method, what is the general solution for a first order differential equation ?

Answer 5

Question 6

Find the general equation

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Answer 9

Question 10

What is the general equation form when the auxiliary equation produces a repeated root?

Answer 10

Question 11

Answer 11

Question 12

What is the form of the general equation when the auxiliary equation gives
1. Purely imaginary roots
2. Complex roots

Answer 12

Question 13

What is the general solution to simple harmonic motion?

Answer 13

Question 15

Answer 15

Question 16

Answer 16

Question 17

Answer 17

Question 18

What is the condition for underdamping and the graph?

Answer 18

When the “a” of the a+bi is negative

Question 19

What are the condition for over damping and the graph?

Answer 19

When the real distinct roots are negative

Question 20

What is the condition for critical damping and the graph?

Answer 20

Repeated root is negative