Breathing exercises aren't necessarily a yoga experience when used for anxiety. Breathing exercises come from different sources, including yoga, meditation, western psychology, Taoism, and other places. So there are many of them. As far as "curing" depression and anxiety goes, that will involve more than breathing exercises. They can help a lot, as can yoga, and meditation, whether from yoga or other traditions is probably better still for this. But to cure it, you have to learn to change the way you think -- instead of thinking anxious thoughts you learn not to, the same with depressed thoughts. This will usually require therapy of some kind and a lot of practice. There's no guarantee of it working, but if you work hard enough and it does work, you will come out the other side. So while I think breathing exercises are really useful and besides they are spiritually rewarding my own view it takes more work than just that for a "cure." But feeling better than you did is pretty cool in and of itself, right? And every positive step can lead to another one until you find that elusive cure. Many have gotten there. I hope you're on of those.
Breathing exercises don't 'cure' anxiety but they help. They slow our heart rate down, calm and soothe us. Here is one to try . . . square breathing (breath in for 4, hold 4, breath out for 4, hold 4, repeat. I can't quite do 4 comfortably, I'm more at the 2 range trying to stretch to 3. :>) but you get the idea).. Here is one I have used with my kids. Birthday candles we call it. Hold up your fingers and blow at the ends of them like you are trying to blow out birthday candles. That's 5 blows. And my son's occupational therapist used what she called 'pizza breaths'. Basically if you are trying to cool food down, you take in a big breath and blow out a big breath onto the food (pizza). :>>) It should help. Give it a try.
How long have you been dealing with depression and anxiety? What else do you do for it?