Well, you could solve it then prove that this solution is unique (not too difficult, I think, since it's a linear equation). Or you could use the existence and uniqueness theorem for linear equations that says that if where are continous functions of on then there is a unique solution to this equation a,b) \rightarrow \mathbb{R}" alt="ya,b) \rightarrow \mathbb{R}" /> with the specified initial conditions on a point.