How do you solve a non-linear diff. equation like this $\frac{d^2y}{dt^2} +A\left(\frac{dy}{dt}\right)^n + By=0$?

Question

I have this non-linear ODE: $$\frac{d^2y}{dt^2} +A\left(\frac{dy}{dt}\right)^n + By=0$$ where $0<n<1$, $A$ and $B$ are constants. Are these two substitution possibilities OK?:

1. If $y=y_1$, $y'=y'_1=y_2$, and $y''=y''_1=y'_2$, then $y'_1=y_2$ and $y'_2=-Ay_2^n-By_1$ for Runge-Kutta method?
2. If $y'=u$, then $u'+Au^n+By=0$? (and how to solve this?)

Is there any other possibility for solving an equation like this? Any reference?

Thanks (again) in advance!

EDIT: Adding some thoughts...

According to WolframAlpha, $u'+Au^n+By=0$ is a Chini-type equation (I've reviewed this too: https://mathoverflow.net/questions/41177/a-nonlinear-first-order-ordinary-differential-equation-ytnat-fracdyt). On the other hand, if we define a new variable $v=u^{-n}$, this equation can be reduced to the equation $$v' -\frac{n\left(B\;y\;v+A\right)}{u}=0,$$ which is a D'Alembert equation according to WolframAlpha, with solution $$v=c_1 \;u^{B\;n\;y} -\frac{A}{B\;y},$$ where $c_1$ is a new constant.

What do you think about this? Is the reasoning OK?