Differential Equations

1 / 12

# Differential Equations - PowerPoint PPT Presentation

Differential Equations. Verification Examples. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB. Verify that the given function satisfies the 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' - claire

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

Verification Examples

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

First compute the derivative:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

First compute the derivative:

Now substitute into the differential equation:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

First compute the derivative:

Now substitute into the differential equation:

This is true, so the equation is satisfied

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

and find a value for C that satisfies the given initial condition.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

and find a value for C that satisfies the given initial condition.

Find the derivative:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

This is true, so the equation is satisfied

Now we need to satisfy the initial condition.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

This is true, so the equation is satisfied

Now we need to satisfy the initial condition.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

This is true, so the equation is satisfied

Now we need to satisfy the initial condition.

Set this equal to -1

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

and find a value for C that satisfies the given initial condition.

Find the derivative:

Substitute into diff. eq.:

This is true, so the equation is satisfied

Now we need to satisfy the initial condition.

Set this equal to -1

Our final solution is thus

We will call this a particular solution because it matches with a particular initial condition.

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB