Hi, i have purchase ipad mini 2 in 2013. But i forgot my apple id and password and it was activation lock, how can i solve it?

Here are the Apple support pages that outline the Activation Lock - and the only mechanisms by which it can be turned off:

Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Turn off Activation Lock – Apple Support

As you will discover, unless you are the owner of the AppleID that was last used to activate the device, you’ll not be able to defeat or bypass the Activation Lock. With documentary evidence that you are the original owner (such as sales receipt showing the serial number), Apple may be prepared to assist - otherwise they and nobody here will be able to help you.

If you have the necessary documentation, Apple have recently introduced a new portal though which you may be able to request release of an Activation Lock:

How to remove Activation Lock - Apple Support & start an Activation Lock support request.

However, recovery of the AppleID credentials should be possible…

If you have forgotten your AppleID or associated password, these can be recovered here:

https://iforgot.apple.com/

To recover your credentials, you’ll need access to any one of the following:

• Your primary email address mailbox that corresponds with your AppleID
• Any of the secondary/recovery email addresses that should be configured for your AppleID account
• Any of the trusted telephone numbers (fixed line or Cellular/Mobile) that are associated with your AppleID

Unless you AppleID account has not been fully/correctly configured, or has been seriously neglected, recovery of the AppleID and password should not be difficult.

More information about recovery of your AppleID:

If you forgot your Apple ID - Apple Support

More information about recovery of your AppleID password:

If you forgot your Apple ID password - Apple Support

When you recover access to your credentials, you would be well advised to log-in to your AppleID account from a web browser - and verify/update any email addresses and trusted telephone numbers:

https://appleid.apple.com/

Unless you have proof of purchase, you're SOL, I'm afraid. The only way to recover an activation locked device without proof of purchase is with your Apple ID and associated password. This is for security reasons - otherwise anybody could take ownership of someone else's device.

It's pretty ancient now, anyway, and wouldn't be able to be updated past iOS 12.5.5 (Apple's version of iOS for legacy devices). Perhaps it's time to replace it...?