The  order of the differential  equations of family of  curves 
$y=C_{1}Si{n}^{-1}x+C_2{\cos }^{-1}x+C_3{\tan }^{-1}x+C_4{\cot }^{-1}x$
(where $C_1,C_2,C_{3}and{C}_4$  are arbitrary constants) is 
 

Here,  $y=C_1{\sin }^{-1}x+C_2{\cos }^{-1}x+C_3{\tan }^{-1}x+C_4{\cot }^{-1}x$
$\Rightarrow y=C_1{\sin }^{-1}x+C_2(\frac{\pi }{2}-{\sin }^{-1}x)+C_3{\tan }^{-1}x+C_4(\frac{\pi }{2}-{\tan }^{-1}x)$
$=(C_1-C_2){\sin }^{-1}x+(C_3-C_4){\tan }^{-1}x+(C_2+C_4)\frac{\pi }{2}$
There are only two independent arbitrary constant order of the differential
equation is 2.