# Second-order non-linear differential equation with polynomial of the derivative

My economic model yields the following second-order differential equation:

$$c_1 (y(x)-1)y'(x) - (c_2 x + x^3 (c_3y(x)-c_4))y'(x)^2+c_5 x^3y'(x)^3 + xy''(x)(y(x)-1)(c_6 + x^2(c_7y(x) - c_8))=0$$

where $c_1, c_2, \ldots$ are known constants an $y(x)$ is the function of interest (it's actually a cdf, so this eventually imposes some boundary conditions).

What is the correct term for such an equation? How can it be solved?