Unqualified domains

So I've got a home network and my own bind install. Let's say my local domain is x, so dodo might be dodo.x, alice might be alice.x, and whiterabbit would be whiterabbit.x. If I ping alice.x or alice.x, they both resolve to the same IP address.

Now let's throw another domain in the mix, accessible over VPN. This domain is also unqualified, and let's call it y, and say it has hosts alpha, beta and gamma, for alpha.y, beta.y and gamma.y.

Now, in Windows, I can tell the system to try resolving unqualified domains with a domain of x first, followed by y. That way, I can ping alpha, and it resolves to alpha.y, and I can ping whiterabbit, and it resolves to whiterabbit.x.

Under Linux, when I try to ping gamma, it doesn't resolve, but when I try to ping gamma.y, it does. Under a Windows VM routed through the same machine, pinging gamma resolves to the same thing as gamma.y. How do I get the Linux host to exhibit the same behavior? (No, I'm not going to route the host's DNS through the Windows guest.)

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:wq