The order of the differential equation of all tangent lines to the parabola y = x² is 

The parametric form of the given equation is x = t, y = t². The equation of any tangent at t is 2xt = y + t². Differentiating we get 2t = y1. Putting this value in the above equation, we have 
$2\mathrm{x}\frac{{\mathrm{y}}_1}{2}=\mathrm{y}+{\left(\frac{{\mathrm{y}}_1}{2}\right)}^2\Rightarrow 4{\mathrm{xy}}_1=4\mathrm{y}+{\mathrm{y}}_1^2$
The order of this equation is 1.