Question

plz answer correctly no fake answers ​

Answer 1

Answer:

( 1 - x² ) d²y / dx² - x dy / dx = 4

Step-by-step explanation:

Given---> y = ( Sin⁻¹x )² + ( Cos⁻¹x )²

To find ---> ( 1 - x² ) d²y / dx² - x dy / dx = ?

Solution--->

(1) plzz see the attachment

(2) First we differentiate given equation with respect to x , using formulee as follows

(a) d / dx ( Sin⁻¹x ) = 1 / √( 1 - x² )

(b) d / dx ( Cos⁻¹x ) = - 1 / √( 1 - x² )

(3) In fourth step we multiplying whole equation by √(1-x²)

(4) In 6th step we again differentiate the equation we get in fifth step and applying product rule as follows

d/dx ( u v ) = u d/dx (v) + v d/dx (u)

(5) In 8th step we use two formulee

d/dx ( √x ) = 1 / 2√x and

d / dx ( x² ) = 2x

(6) In 11th step we multiply whole equation by √(1-x²)