# Continous symmetry group

1. Jun 10, 2006

### eljose

Let be a differential equation :

$$y^{(n)}=F(t,y,\dot y ,\ddot y , \dddot y,..........., y^{n-1})$$

then if we propose a Lagrangian so its euler-Lagrange equation gives:

$$\sum_{k=0}^{n}(-1)^{n}\frac{d^{2}}{dt^{2}}(\frac{\partial ^{n} L}{\partial \ y^{n} })=0$$

The differential equation can be derived from a variational principle...then my question is how could we applycontinous group theory to solve this differential equation thanks,or for example if i know that the differential equation has as a particular solution y(t)=exp(rt) where r can be a real or complex parameter.

Last edited: Jun 10, 2006