The differential equation representing the family of ellipse having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point (0,3) is?

x²/a² + y²/b² = 1
It passes through (0,3), so it will become x²/a² + y²/9 = 1 (1)
Differentiate w.r.t x, we get 2x/a² + 2y/9(dy/dx) = 0
Or 1/a² = -y/(9x)(dy/dx)
Substituting the above expression in the equation (1), we get
x²(-y/(9x)(dy/dx)) + y²/9 = 1
Or, x²(-y/(9x)y') + y²/9 = 1
Thus, -xyy' + y² = 9
Or, xyy' - y² + 9 = 0