I see...
From what I understand about your explanation, that large spaces of functions can be written as a linear combination of variable seperable solutions can be understood by considering the Taylor's series expansions of the solutions. But just another query here - Taylor's series converges...
Hi there,
Does anyone know of a proof of why, in partial DEs, one can assume the existence of variable seperable solutions, then take the linear combination of all of them to be the general solution? Why can't there be any other funny solutions that fall outside the space spanned by these...
Hi there,
Does anyone know of a proof of why, in partial DEs, one can assume the existence of variable seperable solutions, then take the linear combination of all of them to be the general solution? Why can't there be any other funny solutions that fall outside the space spanned by these...