Question about the General form to normal form of Diff Eq

[Saladsamurai]

Homework Statement

The diff eq [itex]x(y')^2-4y'-12x^3=0[/tex] takes the general form. Determine if the equation can be put in the normal form dy/dx=f(x,y)<br /> <br /> Well I have tried algebraically to isolate y' and find that I cannot. So my question is, I have decided the answer is no. Now how do I explain why y' cannot be isolated? Maybe this question is stupid...[/itex]

 

[Dick]

Isolating y' is just solving a quadratic equation. But they have two roots. Does that mean it's not a normal form? That's for you to answer. I don't know.