# differential equations – Very odd results from DSolve for nonlinear ODE

I am solving

$$dfrac{dy}{dx}=dfrac{y^6-2x^2}{xy^2left(2y^3+xright)}$$

In Mathematica 12.2.0.0 on Windows 10, x86, 64-bit

``````  DSolve({y'(x) == (-2*x^2 + y(x)^6)/(x*y(x)^2*(x + 2*y(x)^3))}, y(x), x)
``````

It returns a bunch of root functions like

$$left.y(x)to sqrt(3){text{Root}left(7290 text{#1}^2 e^{5 c_1} x^8-10125 text{#1}^3 e^{5 c_1} x^7+945 text{#1}^4 e^{5 c_1} x^6+2079 text{#1}^5 e^{5 c_1} x^5-735 text{#1}^6 e^{5 c_1} x^4-55 text{#1}^7 e^{5 c_1} x^3+75 text{#1}^8 e^{5 c_1} x^2-15 text{#1}^9 e^{5 c_1} x+text{#1}^{10} e^{5 c_1}+14580 text{#1} e^{5 c_1} x^9+x^{15}-17496 e^{5 c_1} x^{10}&,1right)}right}$$

I was not expecting this, but using step-by-step, we get something like what I was expecting

First, what are you supposed to do with all those root function outputs?

Is there some way to get the step-by-step output?