I have the same issue with my iPad 2. If I stay on a webpage or app for too long the image of the webpage or app I was just using stays on the screen, but for about 10 minutes rather than a few days. I looked up things to fix this and there is a way. Unfortunately, this method is only available for Android devices.
The burn in is caused by pixels getting "worn out" by constantly emitting the same light and not changing for long periods of time. Think of it as not exercising a muscle for a long time. It gets stiff right? Same thing with a pixel.
The solution to this problem is flashing a sequence of colors (RGB and then white). The android app I looked at for this issue on Android devices, called Screen Burn-In Tool, claims that this must be done for at least 8 hours. I would assume that is for worst cases where the burn-in is permanent.
I tried searching the App Store for apps similar to this but to no avail. I am surprised that an app like this doesn't exist on the App Store. If anyone can find such an app please tell me since I have the same problem.