Exact Solution of 2nd order ODE with Fixed Constants: Repeated Roots of Characteristic Equation

[Cerberus204498]

I'm not quite understanding why the solutions of homogeneous equation must be independent?

[numericalmethodsguy]

@Cerberus204498 Go to numericalmethods(dot)eng(dot)u­sf(dot)edu website.  Click on Primer on ODE and read the textbook chapter: A Primer on Ordinary Differential Equations. You will see the answer on pgs 5 and 6 for your question.