Question

form the differential equations by eliminating the arbitrary constants of y=C tan^-1x? plz write all it's steps

Answer 1

$y =c \: {tan}^{ - 1} x$
differentiate with respect to x
$\frac{dy}{dx} = \: c \frac{1}{1 + {x}^{2} }$
that is
${y}^{1} = \frac{c}{1 + {x}^{2} }$

now we get
$\frac{y}{ {tan}^{ - 1} x} = {y}^{1}(1 + {x}^{2} )$
this is the required differential equation