So this is basically the same question as here referring to information provided here. However, I am wondering if this inactive form is always necessary or more of a convenience.
For example, consider the nonlinear ODE $$\dfrac{dy}{dx}\sqrt{\left(\dfrac{dy}{dx}\right)^2+\left(\dfrac{d^2y}{dx^2}\right)^2}+x y=0.$$
Mathematica had some (many) issues with the form above so I tried writing it in the form $$\left(\frac{dy}{dx}\right)^2\left(\dfrac{d^2y}{dx^2}\right)^2+\left(\dfrac{dy}{dx}\right)^4=x^2y^2.$$
This is when I got hit with the message 
Now first of all, it's the first time I have seen an 'Inactive Form' so naturally I turn to google and stackexchange for some help. I'd like to point out that I don't think Inactive form is obvious for some people. The more nonlinear, and therefore, the more complicated the equation becomes, the more complicated and "tricky" the inactive form becomes. As with the linked example the one exponent had to be p-1 so that the grad operator could be introduced, which is not too obvious. It is especially not obvious if you are not familiar with the definition of an inactive form.
So my question really boils down to this. Are equations such as mine and in the linked example NDsolvable without putting them into Inactive Form or are we left with no choice but to put them into Inactive Form. If the latter is the case, how can one easily determine (if possible) the inactive form for complex equations?
In case anyone wanted a 'minimum "working" example' here it is
eps = 10^-3;
NDSolveValue[{(y'[x])^2 (y''[x])^4 + (y'[x])^4 == x^2 (y[x])^2,
y[1] == eps, y[eps] == 0.5}, y, {x, eps, 1},
Method -> {"FiniteElement", "MeshOptions" -> "MaxCellMeasure" -> 1},
InitialSeeding -> {y[x] == 0.1}];
The eps avoids infinity issues, I am also not too worried about the initialseeding. Focus is more on the form of ODES/PDES that are required and if Inactive Form is a "Must" or more of a preferred form.
