Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

x² + y² = ax³

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

y² = 4 a (x – b)

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

y = ax³

Represent the following families of curves by forming the corresponding differential equations (a, b being parameters):

y = e^ax

Form the differential equation representing the family of ellipses having the center at the origin and foci on the x - axis.