The Sturm Separation Theorem for Second Order Differential Equations

We prove the Sturm Separation Theorem for second order linear ODEs. This theorem asserts that between two consecutive roots of the solution to a linear second order ODE, any other linearly independent solution will have a root between the other two roots. This remarkable theorem follows from properties of linearly independent solutions to linear ODEs and their Wronskians.

#mikethemathematician, #mikedabkowski, #profdabkowski