If ( y= ( ⁻¹ x )² ), then ( (x²+1 )² y₂+2 x (x²+1 ) y₁ ) is equal to

Step-by-step solution

Given that, ( y= ( ⁻¹ x )² ) So, ( y₁= d y d x = 2 ⁻¹ x 1+x² ) ( d y d x (1+x² )=2 ⁻¹ x ) ( (1+x² ) y₁=2 ⁻¹ x ) Now, ( (1+x² ) y₂+y₁(2 x)= 2 1+x² ) ( (1+x)² y₂+2 x (1+x² ) y₁=2 ) Since ( y₂= d² y d x² )