# Does the Euler-Lagrange equation have a series solution?

In classical mechanics the Euler-Lagrange equation of motion is a linear homogeneous ODE of second order, how come we do not have a series solution like other famous differential equations (Legendre, Hermite, Laguerre, Bessel etc etc)?

## 1 Answer

To add on to Bey's answer, given a functional, the Euler Lagrange equation becomes an ODE which may or may not be linear or homogeneous. It depends entirely on the system you are trying to model. Series solutions may be useful in some cases.

• Do you happen to know of any sources that highlight this method? – RedPen Jul 18 '15 at 1:06
• Wikipedia is a good place to start. Which method are you referring to? The method of applying the EL equations to a classical mechanics problem, or the method of finding series solutions to such a problem? – Alex S Jul 18 '15 at 1:08
• Series solution to any particular Euler-Lagrange equation that satisfies the necessary linearity and homogeneity conditions required to perform the method of Frobenius really. – RedPen Jul 18 '15 at 1:10