Boundary Value Problem

A boundary problem is an alternative method to solve a second order differential equation not by the two initial values $y(x\_0)=y\_0$ and $y^{\prime }(x\_0)=y^{\prime }\_0$ but instead by using two boundary values of $y$ such as $y(x\_1)=y\_1\text{and}y(x\_2)=y\_2$ Boundary value problems not always have a solution