differential equations n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Differential Equations PowerPoint Presentation
Download Presentation
Differential Equations

Loading in 2 Seconds...

play fullscreen
1 / 45

Differential Equations - PowerPoint PPT Presentation


  • 111 Views
  • Uploaded on

Differential Equations. Separable Examples. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB. Use separation of variables to find the general solution to the given differential equation. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Differential Equations' - rusty


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
differential equations

Differential Equations

Separable Examples

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide2

Use separation of variables to find the general solution to the given differential equation.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide3

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide4

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide5

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide6

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide7

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide8

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide9

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

This C is really eC.

Since it is still arbitrary we can still call it C.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide10

Use separation of variables to find the general solution to the given differential equation.

First, write the derivative in fraction form.

Next do some algebra until all the y terms are on one side and t terms are on the other:

typically you want to leave constants on the t side

Now we can integrate both sides and solve for y.

This C is really eC.

Since it is still arbitrary we can still call it C.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide11

Use separation of variables to find the general solution to the given differential equation.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide12

Use separation of variables to find the general solution to the given differential equation.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide13

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide14

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide15

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide16

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

C is an arbitrary constant, so we can multiply by -2 and still call it C

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide17

Use separation of variables to find the general solution to the given differential equation.

We’ll need to use a substitution for the y integral:

C is an arbitrary constant, so we can multiply by -2 and still call it C

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide18

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide19

Find a particular solution to the given initial value problem.

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide20

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide21

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide22

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide23

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Now we can find the constant from the initial value:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide24

Find a particular solution to the given initial value problem.

We can use a substitution for this integral

First we separate and integrate

Now we can find the constant from the initial value:

Plugging this into our general solution we get

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide25

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide26

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide27

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide28

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide29

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide30

Find a particular solution to the given initial value problem.

Find C from the initial value

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide31

Find a particular solution to the given initial value problem.

Find C from the initial value

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide32

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide33

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide34

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide35

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide36

Find a particular solution to the given initial value problem.

Don’t forget the +/-

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide37

Find a particular solution to the given initial value problem.

Don’t forget the +/-

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide38

Find a particular solution to the given initial value problem.

Don’t forget the +/-

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide39

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide40

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide41

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide42

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide43

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide44

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

slide45

Find a particular solution to the given initial value problem.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB