What will be its differential equation?

y^2-2xy+x^2=a^2

To find the differential equation for the given equation y^2 - 2xy + x^2 = a^2, we need to differentiate both sides of the equation with respect to x.

Differentiating y^2 - 2xy + x^2 with respect to x using the chain rule, we get:

2yy' - 2xy' + 2x = 0

Now, rearrange the equation to isolate y':

2yy' - 2xy' = -2x

Dividing both sides by 2x, we have:

yy' - xy' = -x

This is the differential equation corresponding to the given equation y^2 - 2xy + x^2 = a^2.