I am trying to obtain a solution for $y(x)$ satisfying the following ODE
\begin{equation} y'(x)=\sqrt{Ay(x)^4+By(x)^3+Cy(x)^2+Dy(x)} \end{equation} where ${A,B,C,D}$ are constants. From what I can tell, the solution will be given in terms of elliptic integrals (FriCAS gives an obscure output in terms of the WeirstraussPInverse function) but I am unfamiliar with methods involving those.
Is there any way to approach this kind of differential equation? Thanks!
As @Tyma Gaidash commented, write the equation as $$x'=\frac 1{\sqrt{Ay^4+By^3+Cy^2+Dy}}=\frac 1{\sqrt{A}}\frac 1{\sqrt{y(y-a)(y-b)(y-c)}}$$ and $$\int\frac {dy}{\sqrt{y(y-a)(y-b)(y-c)}}=-\frac 2{\sqrt{c(a-b)}}F\left(\sin ^{-1}\left(\sqrt{\frac{(a-b)(y-c) }{(c-b)(y-a) }}\right)|\frac{a (c-b)}{c (a-b)}\right)$$