I suppose "放す" and "放つ" both mean "let go of something". ／If you let go of something that can go all by itself, I mean like a kind of animal, you can say both of "解き放す" and "解き放つ". ／If it is something that can go only by a kind of human action, I mean like an arrow, a bullet, a voice, a light, etc., you just say "放つ". ／e.g. 矢を放つ、弾を放つ、声を放つ、光を放つ。You usually don't say "放す" with these words.／"解き放つ", which means "release something and let go of it", however, doesn't go along well with these objects above because "解く" here with "放つ" insinuates that you release something that can go all by itself.

Almost same but , 放つ sounds more momentum than 放す. ネコを放す→ A cat is calm ,I put a cat on ground. ネコを放つ→ A cat want to run away, and I put on him ground they sound like that.