Ordinary Differential Equations/Applications to Linear Equations

Existence of SolutionsEdit

Just like with separable equations, not all initial value problems for linear equations have a solution.

Theorem 1: If P(x) and Q(x) are continuous on an interval I containing the point x_0, then the initial value problem has a single unique solution.

This is different from separable equations where the conditions for uniqueness and existence are different - with linear equations, if it exists, it will be unique.

Proof We will use the method of successive approximations just as we did before.

Last modified on 27 November 2010, at 05:29