# Differential equation (Clairaut)

Problem: I have to solve the following differential equation (which is supposed to be Clairaut's): $$y=x(y')^2-\frac{1}{y'},$$ where $$y'=\frac{dy}{dx}.$$

What I have tried: Because it says that is Clairaut's, I proceed by differentiating with respect to $$x$$. With an ideal CLairaut's differential equation, you could "isolate" every term that is multiplied by $$\frac{d^2y}{dx}$$ and, on the other side of the equality, you will get a zero. From there, it easy and you end up getting a family of curves [Link: Wikipedia]. The problem is the square in $$x(y')^2,$$ that messes up everything and I cannot isolate the terms in the right way.

I also tried using Mathematica

DSolve[{y[x] == x (y[x]')^2 - 1/(y[x]')}, y[x], x],


but it gives an error