Form the differential equation by eliminating α and β from (x − α)² + (y − β)² = r²

Find the differential equation of all circles passing through the origin and having their centers on the y axis.

Find the differential equation of the family of parabola with foci at the origin and axis along the x-axis.

Find the differential equation of the family of curves \(y=\frac { a }{ x } +b\) where a and b are arbitrary constants

Solve \(\frac { dy }{ dx } \) = e^x−y+ x²e^{− y}