Macbook Air does not want to update to Yosemite 10.10.3

Try this:

Repair the Hard Drive and Permissions - Yosemite, Mavericks, Mountain Lion or Lion

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

Repair

When the recovery menu appears select Disk Utility and press the Continue button. After Disk Utility loads select the Macintosh HD entry from the the left side list. Click on the First Aid tab, then click on the Repair Disk button. If Disk Utility reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit Disk Utility and return to the main menu. Select Restart from the Apple menu.

Launch the Console application in any of the following ways:

☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)

☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.

☞ Open LaunchPad and start typing the name.

The title of the Console window should be All Messages. If it isn't, select

SYSTEM LOG QUERIES ▹ All Messages

from the log list on the left. If you don't see that list, select

View ▹ Show Log List

from the menu bar at the top of the screen.

Click the Clear Display icon in the toolbar. Then take the action that isn't working the way you expect. Select any lines that appear in the Console window. Copy them to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.

The log contains a vast amount of information, almost all of which is irrelevant to solving any particular problem. When posting a log extract, be selective. A few dozen lines are almost always more than enough.

Please don't indiscriminately dump thousands of lines from the log into this discussion.

Please don't post screenshots of log messages—post the text.

Some private information, such as your name or email address, may appear in the log. Anonymize before posting.

When you post the log extract, you might see an error message on the web page: "You have included content in your post that is not permitted," or "The message contains invalid characters." That's a bug in the forum software. Please post the text on Pastebin, then post a link here to the page you created.