Homogeneous 2nd Order DE from spring pendulum

[DavitosanX]

I'm currently taking a Classical Mechanics course, and we're studying the lagrangian equation. After a few exercises, I thought I'd try to come up with the motion equations for a pendulum where the mass hangs from a spring. The resulting differential equations take a form that I don't really know how to solve. They take the form:

y'' + x*y + g*cos(y) + k/m = 0

and

y'' - (g*sin(y))/x = 0

I would just like to know if these have a particular name, or maybe a specific method to solve them. Thanks for the help!

 

[the_wolfman]

You should check your derivation. The equations that you have don't look right.