 Quote by matematikawan
OK I made that mistake. I should have differentiate [itex]y(x,r)=e^{rx}[/itex] wrt r not wrt x to get the second solution.
So the method also works for DE with constant coeffiecients and it's cool. And why is that I never see this method in a textbook? I always have to resort to the method Lagrange reduction of order to obtain the second solution. Someone need to give a name for this method so that it can be easily refer to.  |
You frequently need to do something like reduction of order as you mention for second order equations. But this method works for
constant coefficient equations. I think if you look in most any elementary DE text in the section about constant coefficient equations, you will find the case of repeated roots of the characteristic equation discussed.