I am a little not clear why Maple's odeadvisor gives [_2nd_order, _reducible, _mu_xy] as an ode type for a second order ode which is already exact as is.
When the ode is exact, then no integrating factor mu is needed (or rather mu=1). But Maple says the ode is "reducible" using an integrating factor mu(x,y)
THis ode is Kamke's 6.78, it is alslo mentioned in this paper in table 1 at page 18
I am just little confused, about the terminology. I thought reducible means the ode reguire an integrating factor of the form mu(x,y) or my(x,y') or mu(y,y') when it is not exact in order to make it to an exact ode so it can be now solved.
Why would odeavisor then says an ode which is already exact is also reducible using mu(x,y)?