Yes this is not at all uncommon error and can normally be easily solved by installing the latest graphics card drivers. However although this is easy with a desktop it is more of a problem with a laptop. Because laptop manufacturers like HP customize the internal hardware themselves you cannot use the graphics drives posted on Nvidia or AMD/ATI support site like with a desktop.
The only graphics drivers that will work on your laptop are those issued by HP on their support site. You don't give any information on your graphics hardware but the only drivers you can use will be posted on HP support site for your exact model number. If you already have the latest drivers installed check HP support site first then as the laptop is still under warranty if you bought it new in august and this is a hardware error then report the problem to HP and they have to sort it out.
I bought a new desktop less than a year ago with a AMD/ATI Radeon HD 5850 graphics card and constantly got the "Display Driver has stopped responding and has successfully recovered" error message and was able to fix it by installing latest drivers from AMD/ATI but as you are restricted to using graphics drivers only from HP then HP have to sort this for you under the warranty. If you already have the latest drivers shown on the HP support site then you can first try re-installing them to see if the error goes away but if not get on to HP. I have never dealt with HP myself and don't know how good their support is.
But don't let them fob you off by saying it is a compatibility issue with some software you have installed yourself. It is definitely a problem with the graphics hardware drivers and is covered by a warranty. They are the only people who can release new compatible drivers for your model to fix this.
No need to buy anything. Simply uninstall and reinstall the display driver, and the video card drivers. Simple fix, as these drivers can easily become corrupted.
Simply takes some time is all. Make sure to download the drivers before hand, and only uninstall and reinstall one at a time.
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