The discussion revolves around determining the order of differential equations, specifically focusing on a given example. Participants explore the concept of order in differential equations, substitutions that may affect the order, and the implications of these substitutions on solving the equations.
Participants generally agree on the method for determining the order of a differential equation, but there is a discussion about the effects of substitution that introduces some complexity and potential disagreement regarding the implications of such substitutions.
The discussion includes assumptions about the applicability of substitutions and the nature of the differential equation, which may not be universally applicable. The implications of reducing the order through substitution are not fully resolved.
ineedhelpnow said:Hello. I can't seem to remember how to do these kind of problems. I need to determine the order of the differential equations. Can someone show how this is done so that I can understand how to do the rest?
$\d{^2y}{x^2}+2\d{y}{x} \d{^3y}{x^3}+x=0$
ineedhelpnow said:Three. Got it. Thanks.
chisigma said:The DE is of third order, of course... but with the substitution $\displaystyle y^{'} = u$ it becomes...
$\displaystyle u^{\ '} + 2\ u\ u^{\ ''} + x = 0\ (1)$
... which is of order two... solving (1) however is a different and not necessarly trivial task...
Kind regards
$\chi$ $\sigma$