i believe you 一定 可以solve this problem i believe you 肯定 可以solve this problem so there is no difference between 一定 and 肯定 but 肯定 also has another meaning，"approve" for example, 他对你的钢琴水平表示肯定 确定 is make sure

一定、definite 肯定sure、和确定make sure

Good question! I'd also be interested in the nuances between them. Edit: Lol, oops, I meant to add this as a comment. Please disregard this post. ;)