Differential Equations (1st Order)

Question 1

What is a first order differential?

Answer 1

One where there is a first derivative

Question 2

Notating and handling constants notation

Answer 2

Question 3

“Verify type questions”

Answer 3

Differentiate (so that no +c to deal with)
Then substitute the original equation into the differential.
To check conditions put on in and just show the other comes out.

Question 4

Answer 4

Two changing variables one expression. Usefulness of proportionality

Question 5

Answer 5

Question 6

What is the separation of variables technique?

Answer 6

When the y can individually be re-arranged to be a coefficient of dy/dx

Question 7

Answer 7

Question 8

Answer 8

Recognising the partial fractions!

Question 9

How do you solve differential equations in the form

Answer 9

Multiply each term by then integrating factor, then it becomes an exact differential

Question 10

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

Answer 14

Question 15

What is the auxiliary equation?

Answer 15

Question 16

What is the form of the general equations when the auxiliary equation produces 2 distinct roots?

Answer 16

Question 17

What is the form of the general solution when the auxiliary equation produces one repeated root?

Answer 17

Question 18

What is the form of the general equation when the auxiliary equation produces complex roots?

Answer 18

Question 19

What are the steps to finding the general solution to a non homogeneous second order differential equation?

Answer 19

Question 20

Special conditions

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

Question 24

Answer 24

Question 25

what is the condition (differential equation) for 1. heavy damping 2. critical damping 3. light damping

Answer 25

1. normal real roots 2. repeated root 3. complex root (impaginary and real component)

Question 26

Answer 26

Question 27

Answer 27

Question 28

Answer 28

Question 29

Answer 29

Question 30

Need previous part (i)

Answer 30

Question 31

Answer 31

Question 33

Answer 33

Separation of variables method