The solution of $${{dy} \over {dx}} = \sqrt {1 - {x^2} - {y^2} + {x^2}{y^2}} $$ is

where, C is an arbitrary constant.

The differential equation of the family of circles passing through the origin and having centres on the X-axis is

The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a, 0), where a > 0, are respectively

What are the degree and order respectively of the differential equation satisfying $${e^{y\sqrt {1 - {x^2}} + x\sqrt {1 - {y^2}} }} = C{e^x}$$, (where $$c > 0,\left| x \right| < 1,\left| y \right| < 1$$) ?