Hello. I took a class on ODEs and learned about solving second order homologous equations by writing down the characteristic equation. http://www.sosmath.com/diffeq/second/constantcof/constantcof.html I am now learning about PDEs on my own and I came across parabolic, hyperbolic, and elliptical operators. Is there a relationship between the characteristic equations from the 2nd order ODEs' characteristic equations and these new PDE operators or should I think of them as two separate ideas? The resources I have come across do not relate it back to ODEs. Thanks.