Differential Equations

1 / 45

# Differential Equations - PowerPoint PPT Presentation

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.

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

## PowerPoint Slideshow about 'Differential Equations' - rusty

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

We can use a substitution for this integral

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

We can use a substitution for this integral

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

We can use a substitution for this integral

First we separate and integrate

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

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

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

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find C from the initial value

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Find C from the initial value

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Don’t forget the +/-

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Don’t forget the +/-

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Don’t forget the +/-

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB