The sum of the order and degree of the differential equation having $y=(sin^{-1}x)^2 +Acos^{-1}x+B, $ where A and B arbitrary constants,as its general solution is :

3

The correct answer is Option (2) → 3

$y=(\sin^{-1}x)^2 +A\cos^{-1}x+B$

order will be 2 (as no. of arbitrary constants = 2)

$\frac{dy}{dx}=\frac{2\sin^{-1}x}{1+x^2}-\frac{A}{1+x^2}$

so $(1+x^2)\frac{dy}{dx}=2\sin^{-1}-A$

differentiating wrt x again

$2x\frac{dy}{dx}+(1+x^2)\frac{d^2y}{dx^2}=\frac{2}{1+x^2}$

⇒ degree = 1, order = 2

sum = 3