Differential Equations (1st Order) Flashcards

1
Q

What is a first order differential?

A

One where there is a first derivative

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2
Q

Notating and handling constants notation

A
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3
Q

“Verify type questions”

A

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.

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4
Q
A

Two changing variables one expression. Usefulness of proportionality

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5
Q
A
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6
Q

What is the separation of variables technique?

A

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

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7
Q
A
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8
Q
A

Recognising the partial fractions!

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9
Q

How do you solve differential equations in the form

A

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

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10
Q
A
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11
Q
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12
Q
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13
Q
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14
Q
A
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15
Q

What is the auxiliary equation?

A
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16
Q

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

17
Q

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

18
Q

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

19
Q

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

20
Q

Special conditions

25
Q

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

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