# "Abel's ODE of the 2nd Kind, Class C"

G

#### Guest

##### Guest
Hello, I have been trying to solve the following differential equation for S(t), where G(t) is an arbitrary polynomial function:

Code:
S(t)=-diff(G(t),t)/G(t)+diff(S(t),t)*S(t)/(c^2-S(t)^2)
The image of this equation is available at http://www.xdemi.com/AOPS.png.

While playing around with Maple 10, the "odeadvisor" of DEtools suggested that this was "Abel's ODE of the Second Kind, Class C". The help file further suggested a transformation of this type to an "Abel's ODE of the First Kind", but I am unsure of what any of this means. I know how to solve ordinary differential equations on Maple, but dsolve() keeps returning nothing, and I am unsure of how to solve this by hand.

Could someone solve this equation for S(t) or refer me to a source of reference that I may find useful?

Thank you very much!

Staff member
G

#### Guest

##### Guest
Thank you. Unfortunately, that is the source that told me what type of equation this was in the first place (Maple Help). I have been trying to use the transform that they speak of, but all I get are errors.

I don't think I am matching up the right functions (f0, f1, f2, f3, g0, g1) with my own functions. Could someone perhaps help with using the information in the link provided above?