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.