Variable transformations

*To*: mathgroup at smc.vnet.net*Subject*: [mg131437] Variable transformations*From*: Nicholas Chisholm <nick.g.chisholm at gmail.com>*Date*: Tue, 23 Jul 2013 04:44:42 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Say I have some differential equation in terms of the independent variable x and dependent variable f(x). Now say I want to do a coordinate/variable transformation where x=x(u) and I want to write my equation in terms of only u and f(u). By pencil & paper, you can do this by applying the chain rule, but I have a complicated equation and I want to check if I've made an algebra slip-up (it involves several dependent and independent variables and up to 4th order derivatives). Is there any way to automate something like this in Mathematica? I've messed around with replacement rules, but I can't get Mathematica to do things quite how I want. Thanks!